In my experience people will start indoors and build experience before heading outdoors.

You could ask people in the bouldering gym whether they have any experience with outdoor bouldering and people will start sharing their favourite spots nearby, and might even invite you along.

Outdoors requires:

- your own climbing shoes

- someone with a bouldering mat

Whereas you will hire shoes from the bouldering gym as a beginner

You won’t need to bring anything to the bouldering gym other than a water bottle and some loose fit clothing

Both! Usually outdoor bouldering is a bit more of an undertaking to get into since you’ll have to travel and bring matts & additional gear. But look up “climbing gym” on google and you should be able to find some if you’re in a reasonably sized metro. Not sure if you’re in the USA but the southwest has a ton of great outdoor bouldering.

It ranges from high tech indoor and outdoor gyms with customisable holds all the way to a random rock somewhere in the middle of nature where local guys put a few mats under. If you start going to a gym you'll naturally learn about all the other places very quickly.