I've been watching people deal with this in their daily routine for a while, and most of the ones who stick with 3 days a week with solid structure end up building muscle just fine. The key thing is that those three days actually count: compound exercises with progressive weight, not just going around doing sets half-heartedly. At two months you're still in that phase where your body responds pretty well to new stimulus, so you don't need to burn yourself out going 5 or 6 days.
What actually matters more than adding days is that each session has quality and you rest between them. Muscle grows when you're resting, not when you're in the gym 😅 If you do 3 intense days with a recovery day in between and sleep decently, you're going to notice changes. Now, if after another couple months you see progress stalling, instead of throwing in two more days maybe it'd be better to switch up your exercises or up the weight. A lot of people stay in the same routine and expect different results, that's what holds most people back.
So the key is being consistent those three days and not obsessing over adding more. Your job and your actual life matter for recovery, so that balance you mentioned is well thought out. Keep at it, make sure you're eating right, and reassess in a couple months if you need to adjust anything.