How to improve SEO without guest blogging

There are plenty of opportunities. Guest blogging is just one of them.

As we have no idea which niche you're in, general rule of thumb is - go find authority websites in your niche and try to get links from there. The best way to do that is to cooperate with site owners. Spamming will not help (your links will be deleted eventually so it's not worth the time). Make sure your links last, so you can increasingly progress your backlink profile.

If you don't have budget for that / you don't have anything you can offer to site owners, participating in discussions is still good way to gain some links. Just make sure you stay on-topic, help other members, bring valuable information... Link here and there (like one link in ten posts) is acceptable, as long as you can bring value to other users on the board.

Good luck!

SEO can be quite tricky if you don't know where to start. Fortunately, you don't have to rely on guest posting alone to get your SEO efforts off to a great start. I think this article on SEO basics would be a great place to start. Good luck!