You can post a photo here so I take a look at the model, because I have the same TTGO and it works perfectly. Maybe something is wrong with the antenna or maybe it is not well connected, try to detach the GPS antenna and put the antenna back. If nothing works, try version 7.11 of the firmware, let me know.
Edit: There is a tiny button cell battery next to the GPS module
Try to measure the battery voltage of the gps with the multimeter.
If the battery is lower than 1.5v your GPS will have a bad battery. if the battery has 2.6v or 2.8v it is ok. The battery is rechargeable, it recharges when you turn on the TTGO, it takes a minute to reach its final voltage of 2.8 ~ 3V keep this in mind.