Javascript – Regex to match at least one of three sub-patterns

I have an identifier that is made of at least one of three parts of various lengths. The first part are capital letters, which can be matched by [A-Z]+. The second part are small letters which can be matched by [a-z]+. The third part are digits which can be matched by [0-9]+. They must occur in this specific order. So all the following are correct identifiers: A, h, 3, Ab, AA9, abc23, Hyy2346. They should be matched by the pattern. Examples of incorrect identifiers include: wD, 99A, 6a5, etc. or anything that contains non-alphanumerical characters.

The problem is that if I do for example [A-Z]*[a-z]*[0-9]* such pattern also matches an empty string which is not a correct identifier. How to make a pattern so that the length of the matched string is at least 1?

This is a simplified version of the more complicated problem I am facing in which I have to match entries in certain ancient scripts. I used [A-Z]+ etc. above as examples to illustrate my sub-patterns, but the actual sub-patterns I have are much more complicated. Nevertheless they are all of the form (a class of characters and words)+. Also: I am doing this in JavaScript. Also: I need to do this in a single regex.

I could try something like ([A-Z]+[a-z]*[0-9]*|[A-Z]*[a-z]+[0-9]*|[A-Z]*[a-z]*[0-9]+) but because my actual sub-patterns are much longer than those [A-Z]+ etc., the result is very long and I am wondering if there is a way to make it more efficient.