Sri Ramanuja argues from the common sense point of view. We only see conscious beings and not consciousness itself. The problem with his argument is that Advaita Brahman is not an object.
Brahma(n)
Manu said, ‘Brahma(n) is not an object of touch, or of hearing, or of
taste, or of sight, or of smell, or of any deductive inference from
the Known. Only the Understanding (when withdrawn from everything
else) can attain to it. All objects that the mind apprehends through
the senses are capable of being withdrawn into the mind; the mind can
be withdrawn into the understanding; the Understanding can be
withdrawn into the soul, and the Soul into the Supreme.’
Mahabharata, Santi Parva, Section CCIV
Advaita Brahman can't be proved because it does not exist as an object but only experienced when the ego dies.
Just look at what is said below about Brahman. Brahman is stated from the negative point of view.
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
Sometimes Brahman is called Satchidananda, existence, knowledge and bliss. Here also Brahman does not exist but makes existence possible, makes knowledge possible makes bliss possible.
It is not possible to prove the existence of Advaita Brahman since it does not exist. It can only be experienced.
Comment:
But when you say Brahman is existence and consciousness please tell me how it exists when atman leaves this Body and doesn't have a form? How can we define the existence and consciousness?
Answer
I have given the sequence after death.
'Just as a man gives up old garments and puts on new ones, so the
embodied self abandons decrepit bodies and assumes new ones.'
Gita 2.22
What happens immediately after death? The answer is given in Gita 15.8 which says,
When he gets a new body or abandons an old one, the Jiva, the lord of
the body, moves, carrying them (the mind and the senses) with him, as
the wind carries smells from their seats (in flowers and the like).
Gita 15.8
The Jiva exists even after death as the subtle body (mind and the senses).
Three stages after death
Listen to the course of a man dying on the earth. The first stage is
that of Ativaha (the subtle body in transit); then that of ghost; then
at the end of a year that of a pitr.
Garuda Purana, Dharma Khanda, Chapter XXX
So the dead person does have a form and thus exists and prana shakti in subtle form accompanies the dead person.
The process of death
Death is inevitable to all living beings in this mortal world.
O lord of birds, when the living beings die, the vital air shrinking
to its subtle size comes out of the throat.
It may escape through any of the nine apertures or through the pores
of hair or through the palate. The subtle soul escapes through Apana
in the case of sinners.
When the vital air escapes, the corpse falls down. When struck down by
death it falls like a tree bereft of its support.
Garuda Purana, Dharma Khanda, Chapter XXXII
Thus there is no problem with the existence of a jiva after death.
Let me finish by commenting on Nirguna Brahman and Saguna Brahman. There have been disputes between Advaita followers and Vaishnavas about their concept of Brahman. Really speaking reality is beyond both according to scripture.
Reality beyond both Advaita and Dvaita
Some seek for the knowledge of non-dual Brahman (i.e. Brahman without
Maya) and some for that of the Dual (Brahman with Maya). But they do
not realize reality is devoid of dvaita and advaita.
Garuda Purana, Dharma Khanda, Chapter XLIX
