This sounds like a settings where you checked to open last page and not the home page when the browser is opened? Did you look at the settings?

Firefox has certain file maintenance tasks it performs at shutdown after you use the Exit command or close the last window. If Firefox discovers at startup that those tasks were not completed, it will perform an automatic crash recovery. So that's the first possible explanation.

You can change how Firefox handles crash recovery: instead of doing it automatically, Firefox can show a screen asking whether you want to restore the previous session. If you start seeing that screen, then this definitely is the problem. Here's how to set that up:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button promising to be careful or accepting the risk.

(2) In the search box above the list, type or paste sess and pause while the list is filtered

(3) Double-click the browser.sessionstore.max_resumed_crashes preference to display a dialog where you can change the value, reduce it from 1 to 0, then click OK

If you use CCleaner, and you have it set to clean up Firefox session data, make sure you have an updated version from November 2017 or later because old versions of CCleaner are not fully compatible with Firefox 56+.