For some comparison of difficulty, there's an old game called Squares which is very similar to yours. It does a good job of ramping the difficulty up pretty fast, but it allows the game have fun short gameplay loops because of the extra gameplay mechanics (ie, you are not just moving but collecting squares too).

Gameplay Video: https://youtu.be/n8nRCyjCy_Y

Apparently you can still play it online at: https://www.albinoblacksheep.com/games/squares2

Have difficulty settings. Default is "easy/moderate" so that people get a sense of it. For people playing twice or as people get more experienced and want a challenge, they can choose a more difficult setting.

Have leaderboards for different difficulty settings to encourage exploration of different settings.

might work out the opposite - 'ah I can do better than that, one more try'

Tbf my experience was the opposite. But sure if I'm just terrible or if it's harder on a phone, but my first tries were sub 20s and my highest was 45 before giving up xD

This is a great use case for using an algorithmic difficulty ramp where it can really dial in that curve to solve for getting people to play longer over multiple sessions.

> There must be some sweet spot there, since if it lasts too little

Absolutely, and therein lies the essence of game design, right?

For a simple game like this, I'd say 8-10 seconds is a good time to shoot for, for the player's first session. It'll naturally get longer as the player gets better. This makes every moment exciting--just a few seconds longer and I can beat my last score. But yes, this is an art not a science.

Just have levels. Each level has more or faster dots. You continue from the last failed level.

berserk mode : move the world, leave the player immobile in the center