Because that wasn't the real reason he came to New York.
This is a somewhat popular fan theory which I feel was best explained by John Granger of Hogwartsprofessor.com over here.
Basically the theory states that, both of the reasons Newt provided for his coming to New York were obviously ruses. (The Puffskien breeder was no longer in business, and the Thunderbird could have been released the moment he arrived.)
Dumbledore is working to defeat Gellert Grindelwald in the shadows — and he has agents working for him in this effort. Newt Scamander is one of these earliest ‘Order of the Phoenix’ members, hence his ability to have a wand though expelled from Hogwarts for cause.
The Back Story We’re Not Told (Yet): Second Thoughts about J. K. Rowling’s Fantastic Beasts & Where to Find Them
The theory goes more in depth, analysing all of Newt's interactions with Grindelwald, and showing the parallels to Dumbledore's views.
Whether or not this theory is true is debatable, but Newt's intro to 2017 edition of Fantastic Beasts and Where to Find Them, definitely alludes to it.
I am not yet in a position to tell the full story of my activities during the two decades that Gellert Grindelwald terrorised the wizarding world. As more documents become declassified over the coming years, I will be freer to speak openly about my role in that dark period in our history. For now, I shall confine myself to correcting a few of the more glaring inaccuracies in recent press reports.
In her recent biography Man or Monster? The TRUTH About Newt Scamander, Rita Skeeter states that I was never a Magizoologist, but a Dumbledore spy who used Magizoology as a ‘cover’ to infiltrate the Magical Congress of the United States of America (MACUSA) in 1926.
This, as anyone who lived through the 1920s will know, is an absurd claim. No undercover wizard would have chosen to pose as a Magizoologist in that period. An interest in magical beasts was considered dangerous and suspect, and taking a case full of such creatures into a major city was, in retrospect, a serious mistake.
I went to America to free a trafficked Thunderbird (....)
It would take months to contradict every other wild assertion in Miss Skeeter’s book. I shall simply add that, far from being ‘the love rat who left Seraphina Picquery heartbroken’, the President made it clear that if I didn’t leave New York voluntarily and speedily, she would take drastic steps to eject me.
It is true that I was the first person ever to capture Gellert Grindelwald and also true that Albus Dumbledore was something more than a schoolteacher to me. More than this I cannot say without fear of breaching the Official Magical Secrets Act or, more importantly, the confidences that Dumbledore, most private of men, placed in me.
Fantastic Beasts and Where to Find Them (2017 edition) - Foreword by the Author
Notice how Newt is quick to deny the claim that he was working for Dumbledore, but then says that giving any more details would violate Dumbledore's trust. While Rita's claim may not be very accurate, it seems that Rowling is trying to hint that there is more to Newt than meets the eye.