Yes, but to see why you have to think about what the evidence actually is, and what a “beginning” actually means.
Redshift, expansion, CMBR is all evidence that the universe used to be much smaller than it is today. The CMBR is specifically a prediction of the claim that the universe was once upon a time so small and dense that it was opaque to electromagnetic radiation because charged particles had not assembled into stable atoms. As the universe expanded, it also cooled enough to allow stable atoms to form, and when this happened electromagnetic radiation could traverse space relatively unhindered. An imprint of this time in the microwave range, also called the surface of last scattering, is now today detectable in the CMBR. It is important to understand that the universe need not have been infinitely small, or to have literally sprang into existence out of nothing, for the CMBR to have formed. All that is required for this is that the universe was very small and dense and expanded from this state of higher density, that’s it. Redshift and expansion are also just evidence that the universe was smaller. You can put the rate of expansion into a coordinate system and draw a line going back to an imaginary T=0 to derive a prediction that the universe was once infinitely hot and dense, but that is an extrapolation beyond the data we actually have. We technically don’t know if time began, or if there was a first moment in the form of a singularity.
Even if we did, that doesn’t help you, because if time literally goes back to a very first moment when the universe was a singularity, then it doesn’t go further. Which means there was never a time at which there was nothing. Rather there was a state of infinitely high density and curvature, but that isn’t nothing. So because the universe has existed for all of time, and since we can’t go back further than time itself, there is no “coming from nothing” that needs to be “caused”. It was never the case that there was nothingness instead of the universe. Rather, the universe has an earliest moment when it was infinitely hot, dense, and curved, and it is incoherent to talk about a before this because there can’t be a before time itself.
Here’s a very simple argument that could be filled out more, but more or less does what’s necessary.
If the initial event responsible for the existence of space, time, matter, and energy has a cause
See this is a problem right out of the gate, because you are treating this problem as if there was some event, a “coming into existence out of nothingness” that needs to be explained. But there is no evidence that there was ever such a beginning. In fact it is logically incoherent to talk about this being the case, as it would imply time itself existed, when there was “nothingness” as the state of the world.