You're probably still in huge lectures like calculus or diff eq, right? I felt the same when I was in your position. I didn't go to a single office hour until 4 semesters in, simply because I didn't need help or could just ask friends for help. I thought it would've been weird to make up a reason to go to office hours and to be honest, I was too mathematically immature to try to strike up a discussion with professors not pertaining to the class material (not that you're ONLY allowed to talk about math).
That being said I wish I did form a relationship with some of my earlier professors, but it didn't come naturally. I actually had some professors for 3 different large lecture classes and they probably still don't know who I am.
It does get easier as you move along in your degree though. After you finish all the intro classes, your classes are no longer in huge lecture halls. You won't be taking classes with engineers and every other stem major. Your professor will actually know who you are since classes are much smaller. This is a big start. During lectures, you can answer and ask questions and the professor can acknowledge that you stand out amongst the rest of the students. Also, classes get harder so you might actually start needing to go to office hours, and you should.
When the time comes, take important and difficult classes (such as advanced ode, pde, noncommutative algebra, or whatever your school has), even if they are not required. Don't use all your math electives on easy blowoff classes. A lot of people will do that, leaving the higher level, not required math classes with 10 or so students. Even though the classes will be harder and take more time, you'll learn so much more. you're going to need to take many of the classes in grad school anyway so you might as well familiarize yourself. Also, the classes look better on applications. Just utilize your resources, including the professors, to make sure you do well in them.
Take the important classes and it will be hard NOT to get to know your professor. Just show that you are interested in the subject, and he or she will take note. You don't have to schmooze them, although that will become easier as well. You can ask them about their research (and hopefully understand what they're talking about) or ask them for advice about grad schools, including what their experience was like. If your school has any sort of research course, take it. You'll get to know the professor very easily, and they'll also get to see your work ethic and gauge what you'd be like as a grad student. Do well and get a recommendation.
Anyway, good luck! Two of my letters were from professors I had during junior year (one of which I took more classes with), so I wouldn't worry too much now if you're having trouble talking to professors, although of course it's better to form relationships earlier. Another important note, keep in contact with the professors you become friendly with after the class is over. They love that. Also they want students to succeed and would be willing to give you advice on the rest of your math career.