“that ”at the beginning of a narrative sentence

That is a demonstrative. It tells you who or what is being talked about.

It may follow the noun to which it refers. “See the red car in the parking lot? That car {the red one} is mine.”

It may follow the concept to which it refers. “We should stand in the shade. That {action} will keep us cool”.

Occasionally it is used to precede, as in the manner of your example. “That I answer here on ELU {a concept} is well-known to readers. That I used to keep bees is {a concept} novel to them”. “That I used to keep bees” is a phrase but not a sentence.

Your example similarly creates a phrase and is incomplete as a sentence. That I don’t know if I am good at making friends refers demonstratively to a concept but says nothing about it. An example of completion might be:

That I don’t know if I am good at making friends shows my lack of self-awareness.