Watch you engine rpm for a while and practice shifting at around 2500 (most often it reads either 10,20, 30 etc ) you will see a set of words on the gage that says X100 20 therefor is 2000 rpm. shift when the needle is between these numbers. Most engines are safe all the way up to 5000 rpm or 50 on the dial front. In time you will feel the point the engine is producing the power best for next shift.

If there was no noise or jerking of the gears or any sounds then you were OK, the chances were that the gears were lined up so your movement slid to the higher gear easily, I have changed without the clutch, just a matter of getting the revs. right for the shift.

You are going to worry yourself to death with that car.

recent questions:

slide the seat forward a bit hard

slammed the door

opened the door but not sure if it was unlocked

drove over cats eyes

I did that in my car for 6 years. After a hundred and seventy three thousand miles it gave up.

You have a way to go yet.

UK

You are going to have to abuse your transmission a lot worse than that to cause any significant damage. Don't worry about it.

When the lights turned green, I got to about 10mph and then shift from 1st to 2nd but in the process of shifting I think I let the clutch out a bit too early while getting into 2nd gear.

I didn't hear any noise from shifting but I am worried of damaging the clutch/gearbox or car components.