The requirements to be elected president will vary country to country. You are correct that the US president must have been born a US citizen on US soil.
In other countries, there may be cases where some allow a naturalized citizen to be elected to a head of state position, but I must mention that many countries define citizenship and naturalized citizenship differently than the US does.
Something you may want to consider is that this has come close to being an issue before in the US. For instance, US Senator Ted Cruz was a major contender for Republican nomination for POTUS in 2016. Cruz was born in Calgary, Alberta, Canada to a father who at the time was a Cuban citizen with refugee status in the US and residency in Canada, and an American-born mother. Cruz moved to the US at age four. Had he been elected, the natural born citizen clause could have been an issue, as Cruz was born in Canada despite getting US citizenship from his mother, and he held dual Canadian citizenship from birth until he renounced it a year after election to the US Senate in 2014.
Similarly, 2008 republican nominee John McCain was born on a Naval base in the Panama Canal Zone, which at the time was under American control. McCain was not a US citizen at birth and was granted citizenship in 1937 at eleven months old.
