Scotty I have a 2003 Corolla with a manual transmission. The car has 130,000 miles on the stock clutch and transmission parts. I’m a firefighter and last night after an aggressive drive to an emergency where I was shifting fast and hard, I found that the Corolla is sometimes hard to shift into 1st from neutral. Like the shifter won’t let me put the car into gear. This only happens occasionally. I just bought the car recently and after some tuning up it runs great and shifts fine otherwise. If it’s something like a throw out bearing or basic transmission part I’m perfectly happy to fix it as I can do it myself.
I have that exact same year, make, model and transmission as you. I find that its very difficult to get it into first and I either have to push or slow down. Being uphill helps go into first better while rolling downhill does the opposite
I believe it is a lockout so that you do not damage the first gear.
Otherwise, post a video of you trying to get into first and show just how much force you have to apply
if you can drive the car wit other great without issues, odds are that your transmission has some issues. I would take the car to a transmission mechanic and have him scan it with his scan tool. In the meantime, do not use the first gear to avoid any possible damage to your transmission.