We’ve known for at least 150 years that we do not live in a physical universe. The universe is certainly real, but whatever it is, it isn’t physical matter. The myth of physical matter was debunked by Bishop Berkeley on logical grounds first, and we have since discovered through both mathematical rationalism and experimental empiricism that the universe is a far, far stranger place than the clockwork atom model would have us believe.
That said, the phenomenological way to answer your question is to simply observe that whatever we experience is real, since what could the word “real” possibly refer to otherwise? There is a Buddhist parable which illustrates this, and which you may find helpful:
“What is this?” asks the Master, pointing to a stone.
“It is the image of a stone which I create in my head, Master,” replies the Student.
The Master picks up the stone and hits the Student in the head with it. “Poor fool,” says the Master, “what a heavy head you must have.”