There is data that at least 40k people have died, and the death rates during lockdown and pre-post lockdown show that without controls the death rate dramatically increases. So, yes, there is evidence that without effort the deaths would increase exponentially, 300K is a pretty conservative estimate if you just let the disease run rampant with zero effort to control, because we would breach hospital capacity, and drugs, plasma and every other medicinal treatment would run out. The data while being incomplete shows the minimum deaths would be much much worse than we have seen.
It also doesn't look at how we would handle long covid health issues which would hit millions of people at the same time without any controls in place.