A webmaster asked Google's John Mueller if Google always crawls the home page of the web site before other pages. The answer John gave was no, Google doesn't always crawl the home page first but he did add that the home page is generally the first page Google finds on a site.
This was on Twitter:
No, but that's commonly the first page we find from a site.
— John ☆.o(≧▽≦)o.☆ (@JohnMu) August 24, 2017
Sometimes a new site might go up and it might get a lot of links to a specific page inside the site. So it is possible Google find the link to the inside page first and then work its way back to the home page after first finding the inside page. It all depends on how Google stumbles on the URLs to your web site. Typically, most of a site's links is to the home page and that means generally Google will first find the home page link.
But this is not always the case.
Forum discussion at Twitter.
