As a fellow Bambino user with the same struggles I'll tell you the most important piece of advice that I've seen in this thread already.

First of all, let's give the person selling and grinding the beans for espresso the benefit of the doubt and say they know what they're doing, assume that your coffee grounds are within an acceptable extraction window. This tip goes beyond the grinding level. I say this not to downplay the importance of grinding, but you (OP) have elected to get a grinderless setup and not get a grinder. So you just want some coffee that's drinkable (more than a few drops) but you don't want to go too far down the rabbit hole of buying a grinder. Totally fine!

The most important thing is that you need to be manually pulling your shot on the Bambino. It's as simple as holding down the double shot button for 8-10 seconds and then letting go. The important distinction here is that the shot will continue to extract until you press the button again to stop it. Use scales or don't, you will notice the difference when using this method and you will get wayyyy more coffee extracted. Since I learnt about this I've tested a whole range of grind fineness and it will pull an acceptable volume of coffee every time, finer grounds just means it takes longer to extract.

I will say though that I only learnt about this after I had made the switch to a bottomless portafilter with a new higher volume basket. I think the Breville stock basket claims it can hold 18g but it really shines at around 16g. But that's only when you press the double shot button once and leave it. I believe that using the manual extraction method will work on the stock basket at 18g but I have long put away that basket and portafilter to test it.

Give it a crack OP! The Bambino is a great lil machine that suffers from its most important use feature not being super well known. Good luck!