You seem to have a misunderstanding what A-GPS means.
A cold started GPS unit needs two different data tables to be able to work - the ephemeris data and the almanac. Updates for these tables are interleaved with the regular navigation data. As GPS data rate is really low (50 bit/s), it takes 12.5 minutes do receive the almanac, longer if you had reception problems during this time span.
Fortunately, the almanac is valid for quite some time (up to 180 days). The ephemeris data is repeated every 30 seconds, but specific for each satellite.
Assisted GPS works around this long start times by downloading the tables not from the satellite, but using a regular mobile data connection. It helps with startup times, but still requires satellite visibility.
Assisted GPS does not use triangulation from cell towers. There are other services like location.services.mozilla.com/ which use Location Area Codes (LAC) resp. Traffic Area Codes (TAC, for LTE) and Cell IDs and sometimes also consider RX power to guess an approximate position. For GSM, the Sierra modules report also neighbor cells (AT!GSMINFO), for UMTS and LTE there is only the currently used cell, thus accuracy is very limited, from a few 100 meters to several kilometers (radius).