It’s up to you to decide whether a character has proficiency with a firearm. Characters in most D&D worlds wouldn’t have such proficiency. During their downtime, characters can use the training rules in the Player’s Handbook to acquire proficiency, assuming that they have enough ammunition to keep the weapons working while mastering their use.

Your artificer has been exposed to the operation of such weapons, your artificer is proficient with them.

Eberron: Rising from the Last War

Enable Firearms in Aurora

You can enable the firearms option from the Dungeon Master’s Guide to grant you this proficiency with firearms just like the option to include feats or allow multiclassing. You can either enable the option when creating a new character or enable it later on an existing character by going to the file menu with your character name in the title bar and clicking Character Options.

Once enabled your artificer will have proficiency with the firearms from the Dungeon Master’s Guide, the weapon proficiency will be displayed on the character sheet, and your proficiency bonus will be applied accordingly. You can add firearms from the weapons category in the equipment section just like any other weapon.