For the GPS, in order to fix much much faster, it required you to has a good connection to the server that contain GPS almanac data, and provide you a good A-GPS support.
https://en.wikipedia.org/wiki/Assisted_GPS

I am not sure whether the meaning of sht GPS problem take how long, for me it take like 10-20s in car without internet connection, and like 1 mins plus if I stay inside the building without going to the windows(even with the helps of A-GPS).
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So in order for testing, I capture the packet, and for my Mi Max 2 MIUI9 China version with flying mode, it download the A-GPS data from
http://xtrapath3.izatcloud.net/xtra3grc.bin
with the header

This seem like the XTRA server for smartphone with Qualcomm chipset, which helps the GPS fix, but it should require more information, so I look at the gps.conf, which is for speed up the fix of A-GPS.

The enabled config are
NTP_SERVER=time.izatcloud.net
SUPL_HOST=supl.qxwz.com

There is a history of android which fixing the slowness of GPS fix by changing the NTP_SERVER to nearest server(like asia.pool.ntp.org, I prefer time.google.com), and also SUPL_HOST to supl.google.com(better don't do this if you travel on China).
As I capture the packet and this connection don't happen, so it will connect if you on your mobile network.

And there is more, as you guys said that changing the APN to 4G fixed it, and yes, there is a config which is


And difference carrier support different standard.
https://xenomorph.net/google/android/gps/