Learn Italian: Vogliamo il risultato velocemente, possibilmente domani. - We want the result quickly, possibly tomorrow.

This follows a specific rule for forming adverbs: if the original adjective ends in -le or -re, you drop the final e before adding the suffix -mente. Since possibile ends in -le, it becomes possibilmente. Because veloce ends in -ce, it keeps the e and becomes velocemente.

In this context, does possibilmente mean 'maybe' or does it mean something else?

While it translates to 'possibly', in requests like this possibilmente usually carries the nuance of 'if possible' or 'preferably'. The speaker isn't expressing doubt that the result will arrive tomorrow; they are requesting that it arrive tomorrow, if at all possible. If you just wanted to express doubt like 'maybe', you would use forse or magari.

Could I place the adverb earlier, like Vogliamo velocemente il risultato?

You could, but it sounds slightly less natural. In Italian, adverbs of manner (which describe how something is done) typically go after the verb, or after the direct object if the object is closely tied to the action. Placing velocemente after il risultato puts the emphasis on the urgency of the request.

Are there more everyday ways to express velocemente in spoken Italian?