Infinite regress problems are a result of a misunderstanding of epistemology. Epistemology is about how knowledge is created, how you can distinguish what ideas you should adopt and act on, and similar problems. Philosophers have commonly tried to solve this problem by saying there is a process called 'justification': a process that can make conclusions true or good or something like that - justificationism. An argument's conclusions are true if its premises and the rules applied applied to those premises are correct. So to show the conclusion of an argument is true, you must show the premises and rules are correct. To do that, you either assert by fiat that they are true, which proves nothing, or you make an another argument. If you make another argument, then you have the same problem as the original argument and you are no better off.
The notion that god somehow solves this problem doesn't make any sense. If you want to use god as a foundation then you either assert stuff about god by fiat, or you argue, which gives rise to the same problem.
Nevertheless, many philosophers ignore or deny or obfuscate this problem and spend their time arguing about induction or god or whatever. They argue endlessly about this issue and you can read vast piles of books about epistemology. People outside academic philosophy may occasionally think something along the lines that this is a difficult problem but progress is being made or something like that and point to some book or other that they haven't read or understood as being the state of the art.
One philosopher who didn't take this way out was Karl Popper. Popper bit the bullet and said that justification is impossible. Knowledge is created by noticing problems, making guesses about the solution, criticising the guesses and using the guesses that survive this process. The truth of those guesses is not guaranteed, nor is it probable or anything like that. But you can select ideas based solely on whether they survive criticism - that is, whether they leave relevant problems unsolved. For a guide to Popper's epistemological work, see