To "make it" means to arrive or to go (I made it to the office just 2 minutes before my boss / Did you make it to the football match? / Are you going to make it to Peter's birthday party on Saturday night? )
So, if you are running around in the morning contemplating your toothbrush (?), or you can't find your shoes or your car keys, you might say "Oh no, I am never going to make it to work!" or "I'm not going to make it to work on time!"
"To make it work" is completely different. In this context, "make it" means "make something happen" and "work" is "to function".
My watch is broken. I took it to the repair shop and said "Can you make it work?" In this context, I meant "Can you repair it?" so "Can you make it so that it works again please?"
It can also mean that you think that something can be done.
"I want one hundred doves released at the end of my birthday party."
"That's ridiculous. Where will we find one hundred doves?"
"One of my friends owns a dove farm."
"And where would we keep them?"
"One of my other friends has a very big cage we could put them in."
"Hmm, OK, maybe we can make it work."
Student or Learner