I know that Brahma, Vishnu, and Maheshwar are representations of creation, protection, and destruction cycles. Do they really exist as entities with a specific appearance?
Good question! But I see a slight contradiction in your wording. You ask about "specific appearance", while at the same time asking whether "they really exist as entities".
Existence is difference from appearance. The substance water exists. But it may appear differently in solid, liquid and gaseous forms.
Similarly, the ultimate absolute reality exists (सत्), but it may appear as different names and forms (नामरूप). You may say that this सत् is not like water, we don't actually see it. But what is actually occurring is that you are experiencing (अनुभव) it. You experience the existence of water through various senses.
Similarly, this सत् is experienced. But this सत् is much more subtle to experience than water. It is experienced not through the senses and conveyed to the mind, but quite in the reverse. सत् is experienced beyond the mind and senses, and then transported back to the level of the mind and senses. The forms and names given to various deities such as Brahma, Vishnu, Shiva, are a result of experiencing the सत् and then bringing back the experience to the level of the mind in various modes.
This is why Rig Veda 1.164.46 says:
इन्द्रं मित्रं वरुणमग्निमाहुरथो दिव्यः स सुपर्णो गरुत्मान् ।
एकं सद् विप्रा बहुधा वदन्त्यग्निं यमं मातरिश्वानमाहुः ॥
The one Existence or Reality (Sat) is named variously by the wise people. They call it Indra, Agni, Mitra, Varuna, Yama, Suparna, Matarishvan, etc.
Taittiriya Upanishad 2.9.1:
यतो वाचो निवर्तन्ते । अप्राप्य मनसा सह । आनन्दं ब्रह्मणो विद्वान् । न बिभेति कुतश्चनेति ।
From which mind and speech return back, not having reached it. Having known this Bliss of Brahman, one does not have any fear.
So you see, experiencing this सत् occurs beyond the mind and speech, but describing it must occur in the mind and speech. Since the mind and speech are as various as the people who have them, we get various descriptions of the same सत्.
Other references in scriptures-
यादृगेव ददृशे तादृगुच्यते ...
In whatever form he is seen, in that form he is described/praised/worshiped...
Katha Upanishad 2.2.9:
अग्निर्यथैको भुवनं प्रविष्टो रूपं रूपं प्रतिरूपो बभूव ।
एकस्तथा सर्वभूतान्तरात्मा रूपं रूपं प्रतिरूपो बहिश्च ॥
Just as the one Agni, having entered the world, shows up differently according to each form, similarly the one Atman of all, shows up differently according to each form."
Chandogya Upanishad 6.1.4:
यथा एकेन मृत्पिण्डेन सर्वं मृन्मयं विज्ञातं स्याद् वाचारम्भणं विकारो नामधेयं मृत्तिकेत्येव सत्यम्
Just as all parts made of clay are known by knowledge of a lump of clay, names are only variations of speech. ‘Clay’ is their only reality.
Do Gods really exist as entities with a specific appearance?
Yes they do, because that is how they are described in the Vedas. For example:
Indra has ever close to him his two bay steeds and word-yoked car, Indra the golden, thunder-armed.
In the Vedas, the gods are described as having a particular body with particular characteristics, and doing various activities that require a physical body.
This is also explained by the Brahma Sutra commentators.
Ramanujacharya in his commentary on the Brahma Sutras says:
Pragâpati with fuel in their hands, staying with him as pupils for thirty-two years, &c. (Kh. Up. VIII, 7 ff.), clearly shows that the devas possess bodies and sense-organs. Analogously, mantras and arthavâdas, which are complementary to injunctions of works, contain unmistakeable references to the corporeal nature of the gods ('Indra holding in his hand the thunderbolt'; 'Indra lifted the thunderbolt', &c.); and as the latter is not contradicted by any other means of proof it must be accepted on the authority stated.
Shankaracharya in his Brahma Sutra commentary:
...[the gods'] corporeality appears from mantras, arthavâdas, itihâsas, purânas, and ordinary experience.
These descriptions should be taken literally because there is no reason to do otherwise.
Do Gods really have a specific (materialistic) appearance?
No. But they can take any appearance based on their will.
I know that brahma vishnu and maheshwar are representations of creation, protection and destruction cycles. but do they really exist as entities?
True, Brahma Vishnu, and Maheshwar are representations of creation, preservation, and merging cycles. And they do not exist as material entities in their original form, but can take the form of any entity if they want.
The everlasting bodies of gods like Brahma, Vishnu, and Maheswara are not in material form. But, they can assume any form by their will, which is generally called as Satya-Sankalpa.
The following are the words of Vasistha about the body of Brahma
All created beings that are produced of a cause, have two bodies (the sukshma and the sthula or the subtile and the gross). But the unborn being which is without a cause, has one body only (which is called the ativahika or the everlasting spiritual body). The increate Brahma is the cause of all created beings, but the uncreated spirit having no cause for itself, has one body for it. The prime lord of creatures has no material body; but manifests himself in the vacuous form of his spiritual body. His body is composed of the mind alone, and has no connection with the earth or any other material substance. He is the first lord of creatures, that stretched the creation from his vacuous body (or spiritual essence). All these are but forms of the images or ideas in his vacuous mind, and having no other patterns or originals in their nature. And that every thing is of the same nature with its cause, is a truth well known to all (from the identity of the effect and its material cause). He is an inexistent being and of the manner of perfect intelligence. He is purely of the form of the mind, and has an intellectual and no material entity. He is prime (cause) of all material productions in the physical world, and is born of himself with his prime mobile force in the form of the mind. It was by the first impulse given by the prime moving power, that this expanse of creation came to be spread in the same ratio, as the currents of air and water (or the velocity of winds and tides), are in proportion to the impetus given to them. This creation shining so bright to our sight, has caught its light from the luminous mind of the formless Brahma, and appears as real to our conceptions (as they are ideal in the Divine mind).
Thus, Gods like Brahma, Vishnu, Maheswara really exist as formless, material-less ativahika bodies as described above.
You may get a doubt of how a material less body can able to create material universe. Vasistha shows an example of dream (jsut) to understand it
Our vision in a dream is the best illustration of this (unreality of worldly things): as that of the enjoyment of connubial bliss in dreaming. It is then that an unreal object of desire, presents itself as an actual gain to our fond and false imagination.
In dreams, our mind or intellect can able to experience the material world, which has no form by itself.