I wasnt able to find anything to support his claim, though I was able to find (rarely sourced) the claim that the life expectancy at birth in the US in the 17C was 35 on a number of not very meticulous websites.
However I eventually found the following study which seems to cover exactly the topic you are talking about, Trends and Determinants of Adult Mortality in Early New England in the 17thC, published in Social Science History: https://www.binghamton.edu/history/docs/Hacker_Trends%20and%20Determinants.pdf
If you look at the Table 1, which gives remaining life expectancy in years at ages 20, 30 and 50 across the entire 17thC, you can clearly see that people who survived into adulthood (20+) generally lived to around 60 or 70.
If you look at the wording, it does seem easy to confuse things:
The Yale graduate survival results also support the mortality literature on the middle colonies, which reports male life expectancies at age 30 in the low 30s, just slightly below most estimates for New England
It might be that your professor has seen this or something like it and confused "number of years lived after 30" with "number of years lived since birth".
So I can't comment on the 1600s because I am on vacation and don't have all my books and notes with me, obviously. But I did just answer a similar question yesterday that was well-sourced.
Your teacher isn't wrong. By 1800, life expectancy was about 37 for anyone who happened to make it to the age of 10. This was lower for those who were enslaved. Heck, it was 49 by 1900! Life expectancy only rises into the 50s/60s with the advent of modern medicine and modern convinces.
Also, be aware that at 1800, only 4.5% of adults lived be in their 60s. This obviously includes infant mortality rates, but it is very striking. Now go back to the 1600s and everything was much more difficult. Supply lines to England were not well-established, winters were harsh and settlers were not fully acclimated, and settlers continued to fight with Natives and each other for much of the 1600s. If you want I can double check some of my books once I return home, but it will be unlikely that it contradicts your teacher.
Please let me know if you have any follow ups.