Assuming your city is functioning well (no/little abandonment, see footnote at the bottom of the post), there are three major bottlenecks:
Yes, there is a 'cap' on population. It's a soft cap that can be raised by building specific buildings, adding city connections, and so on. With an empty city, the Residential caps are:
New buildings will not grow past this amount until you start building parks and so on.See if building parks helps the city expand.
The specific (fairly large) CAP relief list can be found here.
Taxes have an effect on demand. If your tax is higher than the game's coded 'regular rate' then demand is reduced. The regular rate depends on your regional population. Reduce demand by enough and your city will eventually stop growing.
At a population of 0, the neutral tax rate is 9%. It goes down by 0.1% for every 150,000 residents to a minimum of 4.0%.
Since you only have about 600,000 people, your neutral tax rate is at around 8.6 to 8.7%. This should not be a problem.
Do you have zones available for all types (RCI)? Are your taxes reasonable for all types? (E.g. not much higher than 8.5%) Some mayors like taxing dirty industry out of town due to badly written guides. Don't do that, as without an educated populace (which takes a very long time to get) it's the only type of industry that will grow. You can also get farms, but typically only up to a point: The farm cap is 30,000 of each other type and there are no buildings or other things in the default game that raise it. That means farm demand starts at 30,000, and once you have 30,000 sims of other types (e.g. residential) no more farms will grow in the region. The only way to have farms after building your big city is to mod the game.
Without industry, all but the very biggest cities won't be able to get enough jobs to keep growing from just commercial.
I go into more detail about minor causes of recession here