How long does it take before Adsense is approved?

It is extremely difficult to be accepted by Adsense nowadays. Fewer than 5% of applications are approved. So, to have the best chance, you need to be totally committed to your site or blog. Write on a topic which you care about, and which you are knowledgeable about. Don’t write too often – just two or three posts or articles each week for about five or six months, making sure each one is written with very high quality grammar, in your own language (not anything serious or tedious) offering something new – different insights, or ideas, or description of your experiences, or whatever you care about most. Each post should be several hundred words long, written in sentences and paragraphs, and illustrated by own photos- if possible. But probably the most important thing is that you are writing for the sake of your visitors, because you have a topic you care about, and which you want to communicate with your viewers. If you do that, you should start seeing some organic visitors within the first few months. It’s fine to let people know about it on social media while you’re still in the early stages, but what you want is writing that’s good enough that it starts to appear in the top pages of search engines.
After about five or six months, you could then apply for Adsense, and you would have at least some chance of being accepted. But it should never be your sole purpose for writing, so that if you’re refused you keep writing and adding to your site anyway.