How to distinguish between received quadratures
You would need to recover some timing information from the transmitted signal.

A common way is to transmit some sort of preamble before the rest of the data in your frame that is transmitted. The preamble would contain known symbols, so it could be used for multiple purposes, including channel estimation and timing recovery (also known as synchronization).

Once you can recover timing, e.g., from using the received preamble, you can attempt to demodulate your QAM symbols. And besides the phase information that you recover, you also want to avoid any difference in carrier frequency of the signal coming in to the receiver, and the oscillator in the receiver. That's where carrier frequency offset estimation comes into the picture too.