Wa'alaikum assalam brother,
As per islam, as soon as time of prayer starts, say at 2:00pm, then you can pray. its a big mis-conception that start of prayer starts from Adhan. its not like that, Whether there is adhan or not, you can pray salah as soon as time starts.
Adhan in most cases is done for 2 reasons:
Come to pray in majid, as there will be Jamaat ...