Using a wilson booster with my t-mobie 5G home internet gateway

The booster will amplify the signal locally. It cannot do anything about the signal receive power. If it has a small antenna to receive the signal it will only be able to do so much. If the distance from your location to the tower is a long way out you can only get so much speed as the signal will be weaker and of lesser quality and more prone to noise resulting in poor performance. The speed capability always tapers off with distance from the source. It sounds like you have a ver weak signal. With the gateway having a connection only to the source without the booster you should use the T-Mobile home internet mobile application on your phone to gather and record the cellular metrics for the 4G signal. If it is very weak, has poor quality and there is lots of noise the character of the signal will help to explain things and set expectations. 

There are some external antenna solutions that can help improve the reception of signals and make the operation better but that still is an investment and there are the technical aspects of getting them connected IF the gateway you have has connectors for external antenna connections.