You can certainly combine a teleological Creator with a non-teleological selection, insofar as the mechanism itself may have some kind of purpose, but the workings of the mechanism are independent of that purpose. For example, you create a watch to tell time, then there’s a nuclear war, all time-telling organisms are dead, and your watch survives. It no longer tells time, because there is nothing to tell time to, but it still does exactly what it did, independently of the time-telling. The only pre-ordained outcome is deterministic (i.e., a result of the way the watch was put together), and non-teleological.
I think that you have to assume that any teleology will not be an inherent quality of anything, part of its essence, or anything like that. Teleology depends on a purpose, which in turn depends on there being a being for which that purpose can obtain, or it collapses into plain old determinism. The telos of an acorn may be an oak tree, but that doesn’t mean that there is some “purpose” to an acorn, unless someone wants a tree. Likewise, a “purposeless” evolution could be a kind of clockwork universe model, with God setting the spring, then relaxing for a few billion years.
Another analogy. You want a garden, so you go buy a bunch of random seeds - flowers, vegetables, grasses, shrubs, maybe an acorn or two. You go to your plot of land, and just throw seeds all over the place, randomly. Then you wait, and a garden grows. Some plants do well, some do not, but you don’t prune or water, you just let it go. There is a purpose to the garden, in that you wanted to make a garden. But there is no purpose to the carrots growing where they grow, or weeds edging out grass, or bald patches where nothing took. It all may be traceable back to your original purpose, in that there would be no carrots at all if you hadn’t gotten the seeds and thrown them there, but there is no specific purpose to why there are carrots later on, or any purpose to why they grew in one spot and not in another. That is, there will be a kind of evolution to the garden, and the garden might be seen as purposive, but the actual process of the evolution of the garden has no purpose.
Another: let’s say you go for a walk for your health. Where you walk, the places you go and pass by, has no purpose, but the walk itself does.
I don’t subscribe to the idea that there is any such purpose to the universe or any need to hypothesize a Creator much less believe in one, but I don’t think that teleological and non-teleological processes are so contradictory, even in the case of evolution versus God. The distinction between the two, teleological and non-teleological, is conceptual, a difference in how you look at things, not an actual difference between things themselves. Put differently - what is the difference, in principle, between believing in an effective, causing telos and believing in a rain god?
The question is not meaningless, but there is no simple answer. It is probably best, when you have a question that seems like it ought to have an answer, but does not, to question the question. Certainly, some questions are in bad faith, or so difficult to parse that the procedure isn’t worth it - “Why purple monkey dishwasher?” “Have you stopped beating your wife?” and so on. But “Why does the universe exist?” is no one of those. It may lead you to believe that the person asking the question is steeped in error, but that does not mean that the question is meaningless. Off the bat, I’d have to ask “What do you mean by ‘why’?” and then see if the question is malformed.