You are correct. I believe Google penalizes Freenom domains in association with high/inane levels of spam. This is why a paid domain is much more reputable.
I submitted a sitemap and it took about 8 months for it to be indexed.
Then, I got my first Eu.org domain and it took it about 2 months. I do not have any paid domains for any information with those.
Actually I thought google is blocking freenom servers too.
But at their support page they said no freenom is not blocked.
So i think the problem is that the people who take the same domain before you was able to set their sitemaps easly but after the big sitemap changing requests that have been sent to google for the same domain it will take time to recognize that the whole website has been changed.
In addition to that there is no connection between sitemap.xml and indexing.
The robots.txt is the only file that is able to control indexing.
But sitemap.xml will make it easier for google to check the site.
So indexing will take more time without sitemap but it will be indexed at the end.
And you have suggested to use paid domain. Actually i hope i can but i’m from syria and international banks don’t allow us to register for them.
So i have no way to pay.