As other's have mentioned the DMG offers training to get skills as a quest reward. In Tasha's they present an option for swapping a skill. Adventure league I think lets you make any kind of change at low levels.

In addition to joining a thieves guild or apprenticing at a travelling magic show/circus you could even make a pact with a devil or archfey (Not everyone who makes a pact has warlock class levels). Honestly even just spending everyday practising in front of a mirror or with friends could work.

My suggestion would be training with a thieves guild with the pitch being that it ends up with more then just a gold cost for the training. For example maybe you have to join the guild and from now on will occasionally get orders to do certain things that won't be directly at odds with whatever quest your on but would complicate/sink it if you get discovered doing whatever the task is. Maybe it's a single quest/task that you have to do before getting trained. Maybe it's a way of introducing an NPC that is basically treated as a "Bond" from the background section, ie you and the DM agree that during the training you fall in love with a guild member who then serves as a plot hook for several quests, or the opposite you upset someone in the guild and now have a reoccurring rival that will try to covertly sabotage your future quests. It kind of all depends on what the DM wants to do, but the thieves guild provides the most opportunity for them to be creative since it can go in any direction whether it's plot hooks or adding complications or just introducing a cool NPC.