Is it a 1050Ti that requires a 6-pin power connector, or no? Hopefully one of those that does NOT need it. The power supplies on the small form-factor systems usually don't include those.
Do you know what the power supply is rated at? Also, if you can get a look at the side label that shows how many amps are on the 3.3V, 5V, and 12V rails, it will reasonably indicate whether there's enough power available for that card.
The 1050Ti doesn't require a huge amount of power, but some of those power supplies on the small systems are really limited. My Dell, for example, was rated at 220W total, with 18A (thus 216W) available on the 12V rail.