don't have that+noun+that VS don't have the+noun+that

[ahsanul.irfan]

If you don't have that brain that is always curious to know, you can't be what you want to be.

If you don't have the brain that is always curious to know, you can't be what you want to be.

Can I say the first one?

 

[Barque]

I wouldn't use either.

If you don't have a curious mind, you won't achieve your goals. ("Mind", not ""brain".)

Keep it simple.

Can I say the first one?

If I had to choose between your original two sentences, I'd pick the first.