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Then what was the mechanism that ended the Snowball Earth epoch? A NASA article states that CO2 levels are at the highest now then they’ve been in the last 400,000 years.

” In 2013, CO2 levels surpassed 400 ppm for the first time in recorded history.”

https://climate.nasa.gov/climate_resources/24/graphic-the-relentless-rise-of-carbon-dioxide/

But if we go back before 400,000 years ago, there were much higher levels of CO2 in the atmosphere. Here's a quote from an article at Climate Depot:

Princeton’s Dr. Happer, who has authored 200 peer-reviewed scientific papers, explained in Senate testimony in 2009 that the Earth is currently in a ‘CO2 ‘famine.’ Happer explained to Congress: ”Warming and increased CO2 will be good for mankind…’CO2 is not a pollutant and it is not a poison and we should not corrupt the English language by depriving ‘pollutant’ and ‘poison’ of their original meaning,” Happer added. “Many people don’t realize that over geological time, we’re really in a CO2 famine now. Almost never has CO2 levels been as low as it has been in the Holocene (geologic epoch) – 280 (parts per million – ppm) – that’s unheard of. Most of the time [CO2 levels] have been at least 1000 (ppm) and it’s been quite higher than that,” Happer told the Senate Committee. “Earth was just fine in those times,” Happer added. “The oceans were fine, plants grew, animals grew fine. So it’s baffling to me that we’re so frightened of getting nowhere close to where we started,” Happer explained.
http://www.climatedepot.com/2013/05/14/co2-nears-400-ppm-relax-its-not-global-warming-end-times-but-only-a-big-yawn-climate-depot-special-report/

400 ppm CO2 is still quite low, if compared to the geologic record.

I think it is important to distinguish between short term (say, 1000 years or less) cycles, medium term cycles (such as the glacial and interglacial cycles in our present Ice Age), and long term events (generally many millions of years long) such as our current Ice Age (the Quaternary Ice Age, if you want to use Arctic glaciation as the starting point of the present Ice Age, or, more correctly, IMO, the Late Cenozoic Ice Age, using consistent Antarctic glaciation as the signal that the present in-general-cooling trend was well established).

I would note that designating an event or period “long term” does NOT mean it might not have a relatively rapid onset or conclusion, and, as with our present Ice Age, the variations within it can be very large.

It does appear “Snowball Earth”, IF it occurred, was likely ended by a vast release or accumulation of greenhouse gases, but the concentrations are hundreds of times higher than modern values. Many other factors were different too. Comparison of the end of “Snowball Earth” to modern climate variations is not even relevant.

OTOH, ocean levels are not entirely irrelevant. See my next post. The temperature spike in the interglacial immediately prior to the present interglacial is fairly impressive. There is another at approx. 330k years back. Although our present interglacial, so far, looks more like the one 400k years ago, who is to say we could not still get a spike of at least 6 deg. C even without any “input” from humans at all? If anything, what we should concentrate on is creating the most wealthy, powerful society possible, to best deal with whatever Mo’ Nature throws at us...