I think that trial and error is not a good way to go about it. It kind of defeats the purpose.

Firstly, listen hard. Listen until you can sing along in your head exactly what you hear. And keep doing this until you can sing the tune in your head fluently and at will and, most importantly, exactly the way you hear it.

Then what you have to do, once the tune is in your head, is play the bits on your instrument you do know are correct on your instrument. And the with the bits you don't know just sing them in your head. At first, this might be only one or two notes, maybe even only the last note if it's the root. Then, you gradually fill in the gaps as you go round and round repeating it. If you make a mistake with a bit, you play a couple of notes you think are right but you hear they are wrong, make a special effort next time round to not play them, just listen to the voice in your head.

You'll find this method much much quicker and more accurate than flailing round at random. Also, if you try to find the notes by trial and error, it will confuse the tune you have in your head and you might start singing it wrong because your listening to the instrument instead of your voice.

If you keep this up you'll soon get to a stage where your fingers will automatically go where your brain is singing. As I say, it's all just practice.