Is it possible to create fields in a Matrix block from frontend?
There's a lengthy rundown about this in this ticket if you need a detailed explanation.

In short, you'll want to check out P&amp;T's Guest Entries plugin to populate entries on the back-end from front-end input.

I highly suggest paying very close attention to how you should set up your form fields' name attributes from this StraightUpCraft post (scroll to the very bottom for Matrix fields): https://straightupcraft.com/articles/craft-cms-field-guide-twig?view=input