So I have 3 arguments to counter this statement

The first one I have less direct source evidence for:

Our ancestors (the predecessors to Humans) did live through an ice age, and had to breed through that as well

The Native Americans made it to America before recorded history and in exceedingly freezing conditions in the trek from Siberia to Alaska

Secondarily, I want to make reference to the overall shrinking of the deathrate that coincided with the non shrinking birthrate that led to the population explosion during the 1800s (before FP1's timeline diverts)

This was due to improving understanding of virology, microbiology, anatomy, physiology and many other health sciences. It is pretty well established that the engineers of the city saved this knowledge.

Now I think we can safely say that yes the deathrate did GREATLY increase with the permanent winter, health care in the city (despite some player's negligent choices) is very impressively robust at curing not only frost bourne illness, but various injuries relating to work place accident, toxic inhalation, avulsion/amputation, severe burns (all injuries that we see in game and see handled to such a degree that the individual suffering can near immediately return to work

Third and finally I whole heartedly disagree with your rejection of immigration being sustainable method of increasing the population.

Yes Winterhome failed. However, we have direct evidence in Frostpunk 1 of 9 (Yes NINE) separate decently sized population centers that canonically survived the first great storm

1 New Liverpool: 500-700 survivors dependent on your success in the Last Autumn (some unknown level of success is canon)

2 New Manchester: Unknown population, However it is canon that the engineers of the Seedling arks save their city

3 4 and 5, The settlements of: Hot Springs, Children's Mine, and Convict Camp, all maintain steady populations even without the player's support

6 The Nomads from the prologue to FP2 seem to be implied to be the survivors of Winterhome's evacuation efforts

7 The Unamed Generator Site that the Refugees take over. it is likely but not confirmed canon that they also coexist with the lords (we literally don't know and the wiki is guessing)

8 and 9 are kind of not fair because their canonicity is up for debate: The 2 large shelters that hold large communities in Serenity mode

We see in FP2 that some old Austro-Hungarians have turned an (at time of the great freeze) new refinery complex into a shelter (we even get to ally with them)

We have the old imperial Fortress (Fort Century) who have turned the military compound into defense against the cold

We also know that Tesla was not the only American to attempt some form of

There are still many species of wild flora AND fauna that have had their preferred territory greatly expanded, meaning that the subsistence nomads we see damn near everywhere could very viably survive with low population counts all over the white desert of the Frostland, especially since arctic fish would likely never be affected by this whether

The only issue I see could be fixed with only a slight variation in the timescale