Absolutely! In fact "ing" verb forms (called gerunds) are a great way to start a sentence and an alternative way of making your sentences more interesting. Here are some examples:
Running to the office, I swept inside, only to discover the meeting I thought I was missing had been canceled two days ago.
Crunching numbers, she discovered that their payments could be handled by their current budget.
Discovering quickly that they are less prepared to study than they expected, many college students don't do as well their first semester as they had expected.