Can you start a question using 'Meanwhile'?

Meanwhile may be used to start a sentence, but not in the way you have attempted.

“I was absent with illness. Meanwhile, my colleagues dealt with my emails”. Meanwhile here refers to the period during which I was ill.

Meanwhile =

until something expected happens, or while something else is happening:

Cambridge dictionary

Meanwhile has the connotation that something else is, was, or will be happening; during does not.

You have used the word as if it were synonymous with during; this is incorrect usage.

During =

at some time between the beginning and the end of a period:

Cambridge dictionary