I started two weeks ago and I am level 22. At level 22, it takes 100,000 experience to get to level 23, and it starts going up exponentially from there. At level 30, it is absolute hell to get to level 31. Getting to level 20 is relatively easy. Play a few nights a week for a month and you're there.
I wouldn't say the experience gap is a big deal at all. When you're level 10, you should just focus on catching more rare pokemon, don't evolve any rare pokemon that you catch, and don't spend any of your stardust.
By the time you're level 20, it takes so long to level up each time that you can choose a few rare pokemon to fully evolve and push to max CP, then just keep them maxed on CP every time you level up.
By the time you're level 25-30, you should easily have 6 pokemon on your team that are at max CP, and start looking into swapping out your weaker team members for new pokemon that you are evolving or catching.
It's a good structure, and it's been overly criticized a lot. The high level thresholds starting at level 25 do a lot to even the playing field for people who didn't start on Day one. Getting gyms is very easy, so collecting in game money to spend on egg incubators and lucky eggs is actually not that hard (maybe a little slow). Personally, my wife and I both spent 10 dollars on the game to jump start into the higher levels and now we can take gyms easily and easily get 50 game coins a day from the gym bonus.