The reduced mass from clutch to the pistons contributes to the lack of momentum, so little more rpm and a little clutch slip is needed. The clutch is best described as vague on modulating the engagement point. For daily driving I often Start in second.
As Hack says. . . Learning curve. Every stick I've driven has had a different personality. The first time I stepped on the clutch in the GT350, I thought it was weird. It took me perhaps 20 minutes of driving for that impression to go away.
For your situation, I suggest that you don't be hesitant with the gas and don't slip the clutch. Just use little blips of partial engagement and immediately push in the clutch while letting off the gas. That's the best way to move a stick vehicle slowly. I might do this 4-5 times while putting the car in the garage. Left foot / right foot interaction.
As I said, every stick has it's personality. Once you get used to it, this car might well be the easiest stick you've ever driven. I also have a Tacoma pickup with a six speed manual. That one took a while to learn. As evidence, there are continual moans and groans from newbies on Tacoma World about the transmission and clutch. It's not a bad setup; it just has its quirks. And, it's a truck.
FWIW, the large gap in gear ratio between 5th and 6th on the GT350 took me a while to deal with. My truck and a previous car are six-speeds and have evenly spaced gears. Once I learned the GT350, I understood we have a close ratio 5-speed with a heavy overdrive. 6th is really intended for cruising down the interstate. I still find myself dropping into 6th too early, but I'm learning.
Wanted to echo that during a cold start the engine idles higher automatically which means you have more power out of first gear with no additional gas.
Man the clutch is tricky, but after a few days you get used to it. The hard part for me is a cold start in a crowded parking garage because it moves too fast in first gear with the higher idle (and that's after letting it warm up a minute)
I hated the clutch when I first got the car. So much so I bought the Steeda spring the very next day of ownership. Upon the time driving the car and waiting for the spring to arrive, I fell in love with the clutch. Never ended up installing that spring.
Tha 350 has a very tall first gear and a relatively light clutch and flywheel. That said I think the OP is right that the car is a lot more difficult to maneuver when hot in first gear.
I think the idle rpm control is more lethargic when the coolant temp is over 200 degrees.
I have noticed that when the coolant temp is 180 the ecu reacts faster and hold minimum rpm better.