Does the Big Bang Theory still hold weight if time is an illusion?

If time were an illusion then I guess everything would be an illusion.

Time exists in the imagination, only!
If Reality is a Holistic Unity of One, Here! Now!, then what becomes of 'evolution' when there is no 'time' AND there is no 'motion' beyond the imagination?
Of course, all 'theories' are 'concepts, which are 'thoughts', which is imagination! Which works with the 'time' and 'motion' found therein!

"Reality is a synchrony of moments! All Here! Now!"

There is only One (unchanging, ALL inclusive) Reality!

There is nothing 'physical' or 'moving' about the 'Big Bang!', think more a single synchronous moment of Universal Self awareness!
All existence like a huge light bulb going on over the Universal Self!

Even 'illusions' exist, in the imagination. Delusion is the thought/belief that they exist BEYOND the imagination!
'Time' and 'space', 'life' and 'death', Jesus, the FSM, you, me.... all exist in the imagination!

Every moment of existence exists Now!

"The Laws of Nature are not rules controlling the metamorphosis of what is, into what will be. They are descriptions of patterns that exist, all at once... " - Genius; the Life and Science of Richard Feynman
All 'eternity' at once; Now!!

There is only one moment (Planck moment = 10^-43/sec; "almost" one billion trillion trillion trillionths of a second!!!) of the entirety of existence/Reality/the Universe!
All existence, ever, is one, literally, 'timeless' moment!
Now!
One Universal Consciousness becoming Self aware!!

That is why as Reality becomes known, most of our theories and sensory assumptions fade into ignorant dust.

"Be empty of what you know
Your clever mind just whips up
A dust storm of pride.
Allow yourself to be fooled and
peace clowns its way into your heart.

If your head would shatter in wonder
at what Reality really is,
reason’s tyranny would end and
every hair on your head would
become an oracle" - Rumi

Time itself is NOT an illusion. Artificial time-keeping is an illusion.

Time is the 4th dimension of space-time. Three dimensions of space, one dimension of time.

Space and time are properties of physical matter. As long as matter exists, dimension (space) and time have to exist. Time is what quantifies motion through space. All matter is continuously in motion, both sub-atomically, and cosmically. As long as matter exists, motion exists, and as long as motion exists, time exists, whether anyone is around to take note of it and measure events or not. what makes us notice time the most are periodic motions - sunrise and sunset, the period of the orbit of earth around the sun, phases of the moon, movement of tides, etc.

The big bang was the creation of a whole lot of matter and a whole lot of motion in a rather large flash and a very shoert span of time. Time literally was created with the creation of matter. Time began with the "big-bang", the event that created the universe we live in.

One place where time gets a bit weird is when motion gets close to the speed of light. It actually slows down as matter speeds up. This has been shown in actual experiments with atomic clocks on spacecraft being compared to atomic clocks on earth. This difference in elapsed time is in part what Einstein was on about with his theories of relativity, which are essentially about relative motion and relative time between different points of view.

Another instance when time gets a bit weird is at the speed of light. Time stops. The reason is that matter cannot travel at the speed of light, only light (electromagnetic radiation) can do that. Light is not matter, it is energy. Because it is not matter, it has no dimension. Because it has no dimension, time is meaningless for light itself. In other words, if we could ride a light beam as dimensionless beings, we would not experience the passage of time. A practical way to think about this is that a photograph is a picture of light that has bounced off of physical objects and has been captured by a camera sensor or film. The light, and the reflected objects are motionless and frozen in time. Photographs are quite literally "timeless'.

Anyway, enough of the weirdness part of it. Time is not an illusion. It is part and parcel of the big bang and is one of the 4 dimensions that make up reality for us..

It's called space-time for a reason. What we see is not what is happening right now, just echoes of what did happen, with the most recent being the closest. Time is relative to gravity also, so something that dense as the start of the big bang would have it's own time.
You might like to ask why space isn't white - if the big bang is the furthest thing we could see.

So if time is only in our minds, and when minds did come into being, the universe suddenly popped into existence, with stars and planets moving around?

Unless you're going to claim that stars and planets have minds, to create time?

Science is based on the concept that there is an objective reality "out there", not depending on our minds. And this objective reality has time and space.

Yes, but in a different context.

Time is an illusion here on earth. It is of no essence universally. :D