Currently a paid subscription is required in order to play the GeoGuessr. The daily challenges are available to play for free, but those are quite limited.
One of the ways to play GeoGuessr for free is to join a party which is hosted by a paid subscription user. This option is not easily available for everyone.
The best way to play GeoGuessr for free is to play challenges created by other users. Here are the challenges that you can play for free at any time.