The physical universe, by our best theories, preceded all the minds we know about.
Mentality, at least the mentality we know of, arose out of what preceded it. There weren't solid
things for a long while (sorry, don't have the numbers) and as far as we know, mentality
requires a physical basis that didn't yet exist. So there doesn't seem to be a mind
for the universe to be inside of, at least not for a long while.

Of course this doesn't prove materialism, but the idealist owes us some account of
what the mind is that the universe was 'inside' from the first. Also what the relation
was to that mind. Speculation is cheap, one needs something more persuasive.

If the mind is God's, then we need good reasons to think God exists. Idealism
is weaker if it commits us to theism, as it entails something
very controversial. Also we need reason to think that God didn't
create a world that could exist 'outside' his mind, in the sense that he
didn't have to perceive it for it to continue. Most Western scripture suggests
that God created a mind-independent world, one he knows everything
about but doesn't depend on his perceiving it to exist. Certainly he had the power to do this.
Why wouldn't he?

If it isn't God's mind, whose is it? And science has generally erred away
from supernatural explanations. Idealism is in some tension with Science,
it would seem.

Generally science has proceeded successfully on the supposition that
there is nothing about material things that requires them to be perceived
to exist. What would it be, anyhow? Why would they need to be
perceived. On the face of things, there is nothing about them that
cries out for that sort of explanation. Again, even if they
were created somehow, that doesn't mean they must be perceived
to exist.

The onus seems to be on the Idealist to motivate idealism.