The British Ministry does not care about underage magic, before students go to Ollivander. Is MACUSA stricter on preschool magic?
It’s unclear - but MACUSA was stricter on school-aged wizards.
It’s unclear what the rules for young wizards under eleven who haven’t started at Ilvermorny yet are. However, laws in America are certainly stricter, as (though the law may have changed in 1965) American wizards aren’t allowed a wand until after they’re sorted into their house at Ilvermorny, and are legally required to leave their wands in Ilvermorny until they turn seventeen.
Once students have been allocated a house they are led into a large hall where they select (or are selected by) a wand. Until the 1965 repeal of Rappaport’s Law, which enforced very strict conformity with the Statute of Secrecy, no child was allowed a wand until they arrived at Ilvermorny. Moreover, wands had to be left at Ilvermorny during vacations and only upon attaining seventeen years of age was the witch or wizard legally allowed to carry a wand outside school.
- Ilvermorny School of Witchcraft and Wizardry (Pottermore)
America does certainly have stricter laws for school-aged wizards, as they don’t allow young wizards to have wands at any point outside of Ilvermorny. However, how MACUSA handles underage magic done by wizard children who haven’t started going to Ilvermorny yet isn’t clear.
MACUSA didn’t tolerate magic phenomena, that may apply here.
Though children of that age often can’t control their magic, so can’t truly be ‘blamed’ for it, it’s unclear if MACUSA would consider that, as they’re also intolerant of magical creatures, most of which are also ‘innocent’ and not trying to flout the Statute of Secrecy or reveal magic to Muggles.
MACUSA was also more intolerant of such magical phenomena as ghosts, poltergeists and fantastic creatures than its European equivalents, because of the risk such beasts and spirits posed of alerting No-Majs to the existence of magic.
- 1920s Wizarding America (Pottermore)
It’s likely that their intolerance towards magical phenomena in general, including ones that couldn’t help it like magical creatures, would have some effect on their treatment of young wizard children’s accidental magic. It seems very likely they’d be at least somewhat stricter on it, though it’s unclear exactly how they handle it. With their general stricter stance on magical phenomena, though, it seems very likely that their laws about young wizard children would be stricter than Britain’s.
It does not seem possible to prevent children from performing uncontrollable magic
That's the point, isn't it? Small children start to use magic instinctively - that's how you know they are wizards. Seems like magical abilities can be shown at pretty young age, before one can explain the child about rules and law.
A tiny boy no older than two was crouched outside a large pyramid-shaped tent, holding a wand and poking happily at a slug in the grass, which was swelling slowly to the size of a salami.
Does not seem possible to imply any restrictions on their behavior, apparently they often even do not realize what they are doing (remember Harry's curious cases before he found out he was a wizard).
Moreover, remember it's dangerous to prevent children from performing magic (Ariana and Credence are good examples)
Thus, controlling pre-school magic should be up to parents.
Which is pretty much the same as in Britain. Thought we do not know how strict is the punishment for careless parents in each country.
Before the repeal of Rappaport's Law students weren't allowed wands outside of school.
Until the 1965 repeal of Rappaport’s Law, which enforced very strict conformity with the Statute of Secrecy, no child was allowed a wand until they arrived at Ilvermorny. Moreover, wands had to be left at Ilvermorny during vacations and only upon attaining seventeen years of age was the witch or wizard legally allowed to carry a wand outside school.
- Ilvermorny School of Witchcraft and Wizardry - Pottermore
We can't be sure about what the laws were like after the revocation of Rappaport's Law. But since they are saying the word "until" it might be safe to assume that things changed with magic after the change in laws. Macusa was modeled on The Wizards council of Great Britain but that predates The Ministry of Magic so we cant be sure about their underage laws.
MACUSA was modeled on the Wizards’ Council of Great Britain, which predated the Ministry of Magic. Representatives from magical communities all over North America were elected to MACUSA to create laws that both policed and protected American wizardkind.
- The Magical Congress of the United States of America (MACUSA) - Pottermore