Not on a free link, and that is deliberate. A free dochost page expires after seven days, so it is served with a noindex tag: letting Google index a page that is about to disappear would leave a dead search result behind it.
A page can be listed in search when all of these are true:
- it is permanent — pages published on a paid plan never expire;
- you set Search engines to Listed in that page’s settings. It is off by default, so nothing you publish ends up on Google by surprise;
- it is public and has no password.
When a page qualifies, the noindex tag is gone the next time it is crawled. Google still decides when, and whether, to show it: a brand-new page with nothing linking to it can take days or weeks to be picked up.
If what you want is a free site that Google indexes, a static host on your own account — GitHub Pages or Cloudflare Pages, compared below — is the honest answer. Nothing expires there, so there is nothing to keep out of the index.