That just reveals you don’t know what evidence actually is. Yes, evidence can vary in likelihood depending on the hypothesis. Evidence is data that is more or less likely to be produced, depending on whether some hypothesis is true or not.
To give a simple example, consider the two hypotheses:
A) This coin is extremely biased and lands heads up 99% of the time and tails 1% of the time.
B) This coin is fair and only lands heads up 50% of the time on average.
On which hypothesis it is more likely to obtain the following evidence (a sequence of coinflips)?
HTTHTHTTTTHTTTHHHHHTHTHHTHT
It should be intuitively obvious that you’re more likely to get that sequence of conflips, which is evidence, on the hypothesis that the coin is fair. As we can also see, the evidence has a probability, a likelihood of being obtained, that depends on which hypothesis is true. If A had been true, that sequence would have been much less likely as we’d pretty much have expected a sequence of only heads in those 27 coinflips(since it would take, on average, 100 flips to get a single tails).
That also means the sequence of coinflips is evidence FOR hypothesis B over hypothesis A, and actually evidence AGAINST hypothesis A.
So now that you too understand how evidence works, you can proceed to show that this putative evidence that the universe had “a beginning”(whatever you mean by that) is more likely on the hypothesis that God exists than on any competing hypothesis.