These are all used to give reasons.

"Because" is more common than as or since, and we use it when we want to focus on the reason.

I'm tired because I didn't sleep very well.

When we want to give extra focus to the reason, we can put the because clause at the beginning of the sentence.

Because my bed is uncomfortable, I'm getting a bad back.

"As" and "since" are more formal than because, and we use them to focus on the result rather than the reason.

I hope Tom's brought that comic as I wanted to borrow it from him.

Noodles are popular since they're easy to cook.

We often use "as" and "since" clauses at the beginning of the sentence.

Just remember to add a comma.

So, as our minute is up, I'll finish recording this video.