Scientists are generally highly intelligent and well educated people who are not likely to risk reputational suicide by being sloppy with their conclusions. One of the greatest upsets in the field of Cosmology during the past fifty years has been the discovery that the galaxies are moving apart at an accelerating rate.
They are thorough in their observations, careful with the hypotheses they formulate and painstaking when it comes to arriving at some theory. If there's general agreement that the Universe is 14.6 billion years old, we can be very confident that it is close to the actual age.
You look at a rate and distance when we are talking about how it all started; you do not know where it was when it started, and you have no idea if it was created fully with the light between the stars and earth already being seen. If it started with a singularity, then still, seeing the rate and calculating distance does not give us any insight into those questions. Your starting point is the mystery that is not explainable by how old you think the universe is; age does not give us any insight into the beginning; even if the universe is as old as you think it is, that does not answer how and why it is here.
Well, we might not know precisely "when" it started. But if the Universe existed 13 billion years ago, then we can safely assume it started sometime before that. And we can still watch in the Universe unfold since it started. that is a little field of science called "cosmology."
As for why? Well, mankind has been fighting wars and slaughtering each other for 6,000 years, trying to prove their "God(s)" was more right than everybody else's. And we are still no closer to a consensus now than we were back then. Maybe another 6,000 years of warfare will get us an answer?
Not knowing how and why it started really puts us at a disadvantage to know how old it is. Which is the main reason I don’t argue for some amount of time and make a declaration about age. I use to argue for a young Earth but don’t any more, there is nothing I can point to in my opinion that can give us that type of insight. As I pointed out seeing a rate does not mean it has always been doing that, that is a different question.
The God question is raised when we look at the universe, how the precision in it is so tightly bound in a variety of forces holding it all together. It is not a master of we don’t know so God did it, it is a matter of what we know and a great nothing cannot explain it.
Deep time does not answer highly complex processes with very short viability times before degrading begins.