You don't use a comma after perhaps. But there are exceptions to this exception!
Linguaholic gives examples that I can modify
Why did they not bring an umbrella?
Perhaps they thought it wasn't going to rain.
Did they get wet?
Perhaps, they thought it wasn't going to rain.
In the first case, with normal punctuation, the speaker is unsure about what they thought. In the second case the speaker is certain they thought it wasn't going to rain, but not sure if they got wet.
So there are examples in which "Perhaps" is followed by a comma. But they are rare. Normally there is no comma after an introductory "perhaps", and in your example there should normally be no comma.