Generally speaking, most young birds 'found' abandoned at this time of year are not abandoned at all- the parents are nearby and will contine feeding them. Unfortunately most 'abandoned' birds rescued by well meaning people will die through malnutrition. They are ALWAYS best left where they are found.
However in your case if it has managed to get indoors then you can hardly leave it indoors!! Try putting it outside- its calls will attract the parents - however nature can be cruel and you will likely find a dead bird in the morning.
If you feel you must feed it then be prepared for hard work. Blue tits are seed and insect eaters but will only feed insects to their young. So either start collecting insects and slotting them down the bird with a pair of tweezers. Or get a pint of maggots from the fishing shop and chop them if they are too big. I once raised a starling which fledged and flew- long hard work at all hours of the night and day! When it flew it joined a flock of starlings- flew back and landed on my head as if to say bye and flew off with the flock- quite moving!