1)"Being recognized worldwide, the theory tremendously impacted other sciences."
OR
2)"After being recognized worldwide, the theory tremendously impacted other sciences."
OR
3)"The theory tremendously impacted other sciences after being recognized worldwide."
Would you stick to "impact" or "have an impact"?
I think all of your sentences sound great. I would not change to have an impact. But could you? Of course. Writer's choice here.
Not a teacher
The use of impact as a verb seems to be a rather recent American development. Searching the BNC for the phrase impact the produced only 43 instances and in all but a small handful impact was used as a noun.
In Canada I think we would strongly prefer have an impact on, and I can say for certain that would be my strong preference.
NOT A TEACHER.
The verb "impact" is sometimes used with the prepositions "on" or "upon" as well.
"That would impact negatively on the state of affairs."
I think this use of "impact" is most common in legal writing. I would suggest that you avoid it.
I started hearing it on American news channels a few years ago, and it stood out the first time as I hadn't come across it and it did sound strange, but it's becoming very common, and it is appearing regularly in BrE now. It's economical, clear and catchy, so I can see it becoming widely adopted. I have found myself saying it, though I would still use have an impact on in writing.