If Brahman is nirguna, how are we even sure that such an entity or state exists?
And if it does exist, then isn't "existence" one of its attributes (guna)? Then how can we say Brahman is Nirguna?
Nirguna Brahman does not exist. It is Satchidananda. Here Sat means existence itself, chid means consciousness itself and ananda means bliss itself. It is impossible to say anything about Brahman.
The Upanishad also says that Brahman is pure consciousness, devoid of other aspects contrary to this, and without any distinguishing features, as in, “As a lump of salt is without interior or exterior, entire, and purely saline in taste, even so is the Self without interior or exterior, entire, and pure Intelligence alone” (Brhadaranyaka Upanishad IV.v.13), which means that the Self has no internal or external aspect apart from pure consciousness, Its nature being mere impartite consciousness without any interstices. Just as a lump of salt has the saline taste alone both inside and outside, and no other taste, so also is this Self.
Brahma Sutra Bhasya of Sri Sankaracharya III.ii.16
Nirguna Brahman can only be expressed in negation.
Moreover, the Vedas reveal through a negation of other aspects that Brahman has no distinguishing feature, as for instance in, “Now therefore the description (of Brahman): ‘Not this, not this’” (Brhadaranyaka Upanishad II.iii.6), “That (Brahman) is surely different from the known; and, again, It is above the unknown” (Kena Upanishad I.4), “That Bliss of Brahman, failing to reach which, words turn back along with the mind” (Taittiriya Upanishad II.ix.1), and so on. And it is also known from the Vedic texts that Badhva being asked by Baskali, replied merely by not uttering a word, as stated in, “He (Baskali) said, ‘Teach me Brahman, sir.’ He (Badhva) became silent. When the question was repeated a second and a third time he said, ‘I have already spoken, but you cannot comprehend. That Self is Quiescence’ “. Similarly in the Smritis, the instruction is given through a negation of other things, as in, “I shall tell you of that which is to be known and by knowing which one attains immortality. The supreme Brahman is without any beginning. It can neither be called gross (visible) nor fine (invisible)” (Gita XIII.12), and so on. Similarly the Smriti mentions how Narayana in His cosmic form said to Narada, “O Narada, that you see me as possessed of all the (five divine) qualities of all elements, is only because of My Maya, called up by Myself. For else you should not understand Me thus.”
Brahma Sutra Bhasya of Sri Sankaracharya III.ii.17
Brahman according to Yajnavalkya
Yajnavalkya said: O Gargi, it is the supreme being that the non-yogins call gross but, in fact, that is eternal and wonderful lord; one that is not long, not red, that has no head, that has no setting, hence that has a lasting taste, that has no contact, no smell, no juice, no eyes, no ears, neither speech nor mind, no brilliance, no proof [or magnitude], no (worldly) happiness, no name, no race, no death, no age, no ailment; that is nectarine, that is expressed by the word Om, that is immortal, that has neither a predecessor nor a successor, that is endless and non-external. It eats something. It does not eat anything. ..
Linga Purana II.9.53–54
Brahman does not exist but is the source of all existence. Brahman, however, cannot be described in any manner.
MASTER: "Brahman is beyond vidya and avidya, knowledge and ignorance. It is beyond maya, the illusion of duality.
"The world consists of the illusory duality of knowledge and ignorance. It contains knowledge and devotion, and also attachment to 'woman and gold; righteousness and unrighteousness; good and evil. But Brahman is unattached to these. Good and evil apply to the jiva, the individual soul, as do righteousness and unrighteousness; but Brahman is not at all affected by them.
"One man may read the Bhagavata by the light of a lamp, and another may commit a forgery by that very light; but the lamp is unaffected. The sun sheds its light on the wicked as well as on the virtuous.
"You may ask, 'How, then, can one explain misery and sin and unhappiness?' The answer is that these apply only to the jiva. Brahman is unaffected by them. There is poison in a snake; but though others may die if bitten by it, the snake itself is not affected by the poison.
"What Brahman is cannot be described. All things in the world — the Vedas, the Puranas, the Tantras, the six systems of philosophy — have been defiled, like food that has been touched by the tongue, for they have been read or uttered by the tongue. Only one thing has not been defiled in this way, and that is Brahman. No one has ever been able to say what Brahman is."
The Gospel of Sri Ramakrishna, Visit to Vidyasagar
If you want to be sure of It than you will have to do the necessary spiritual practice. There is no other way.
For the unrealized, the truth of Nirguna Brahman can be apprehended only from a realized person's physical proximity.
All the words written about it, like the Mahavakyas are only pointers.
SANKARACHARYA AND HIS FOOLISH DISCIPLE THE great Sankaracharya had a foolish disciple who used to imitate his Master in all matters. Sankara uttered 'Sivoham' (I am Siva); the disciple also repeated „Sivoham’. To correct his disciple's folly, Sankara one day, while passing by a smithy, took a potful of molten iron and swallowed it; and he asked that disciple also to do the same. Of course, the disciple could not imitate this act of his Master, and thence forward he left oil saying „Sivoham’. (52)
The words are the same - Sivoham (I am Siva) - but it means something different when uttered by the realized and the unrealized.