While I agree to some extent with your point, I think your definition is far too strict. For example, by your definition, the UK is currently and has always been a tyranny, since they don't have a formal constitution in the sense of any US-style state.
However, I do think you're generally right - even under a more relaxed definition of what does or doesn't constitute a tyranny, the USA is clearly one of the first non-tyrannical states, at least among those that still exist today. The UK had a mostly-democratic ruling system for even longer than that.
On the other hand, if we define tyranny to refer to any state in which elections are restricted to a relatively small subset of the population, then the USA or UK are not that early. Voting in the USA was largely restricted to male property owners until 1840. Many other countries had adopted at least universal male voting by this time. The UK was even later to pass this standard.
However, I do think you're generally right - even under a more relaxed definition of what does or doesn't constitute a tyranny, the USA is clearly one of the first non-tyrannical states, at least among those that still exist today. The UK had a mostly-democratic ruling system for even longer than that.
On the other hand, if we define tyranny to refer to any state in which elections are restricted to a relatively small subset of the population, then the USA or UK are not that early. Voting in the USA was largely restricted to male property owners until 1840. Many other countries had adopted at least universal male voting by this time. The UK was even later to pass this standard.