TinyGPS won't work until you are receiving characters and have the correct baud rate. Try this simple program, which will just echo what is received on the serial port:
void loop(){
if (gpsSerial.available())
Serial.write(gpsSerial.read());
}
Make sure the ceramic antenna (not the labeled portion of the unit) has a clear view of the sky and you are out of doors. You will get nonsense characters if TX on the GPS is connected to RX on the Arduino, but the baud rate is wrong, but if nothing appears on the serial monitor (and the LED is blinking), the connections are wrong. Fiddle with that until you receive clear messages from the GPS. Then make sure the messages contain latitude and longitude -- they won't until the GPS has a fix. Then you can use TinyGPS.
Finally, try the GPS unit on 5V instead of 3.3V. The Aliexpress page says (why 3.5V?)
Wide voltage range: Mains of +3.5 V ~ +5.0 V, owned RTC power
Bottom: 25 * 25 * 4mm ceramic antenna
Output data baud rate 4800bps or 9600bps or customized according to customer requirements