The oceans on early Earth were not even close to freezing, they were actually near scalding (that is, if the atmospheric pressure was the same as today, probably it was much higher so it was not even evaporating too much even at ~50°C). Plus, Earth at that time had a lot of volcanism and an atmosphere very rich in greenhouse gases. It is not surprising to me that early Earth had oceans with recieving 70-80 percent as much radiation from the Sun, considering Mars probably had oceans at that time as well, and it recieved only cca 30-35 percent of radiation compared to present day Earth (it recieves cca 45 percent at present time). It is nonsense to make calculations based on present day Earth, hell, TITAN is hypothetised to have liquid water oceans when it was very young, despite recieving less than 4 percent of Solar radiation at Earth, why? Internal heat. Hell, even moons of Neptune and Uranus probably had liquid water oceans for a while in the same way Earth was initially molten with lava. Atmospheric models were made for Gliese 581 d that support liquid water even through it recieves only 27 percent of Earth-level stellar radiation.
If scientists continue to speculate over "problems" like this, they'll soon announce that Earth is not supposed to be habitable at all.
There is even evidence that Earth was even hotter than "just" 50°C, at 60-70°C in the Archean.
I find these arguments and "paradoxes" to be contrived and nonsensical. It is just like the argument against extraterrestrial extremophilic life "BUT life must first evolve in NORMAL conditions". Fine, except that "normal conditions" at the time life arose on Earth were a scalding acidic oceans full of hydrogen cyanide, an atmosphere full of CO2 and methane and extreme volcanic activity. And this was actually GOOD because abiogenesis would never occur on present day Earth. Present day Earth is extremely good for nurturing, evolving and reproducing life, but if it was the same way 4 billion years ago, life would never arise. That is why hot water termophilic acidophiles are probably the closest thing to first Earth life. In short, for abiogenesis, you need "extreme" conditions. Free oxygen and neutral ph water is good for making life thrive to unimaginable heights, but very bad for actually creating the first DNA molecule and cell from scratch.
I think the term "primordeal soup" fooled too many people to believe early Earth must have been cosy and clement. If you drank this "primordeal soup", your stomach would have melted and you'd die of poisioning at the same time.
When first photosynthetizers created enough oxygen, the Earth froze for a while. But the good thing was that at that time Sun was already brightening. Life creates optimal conditions for itself as long as it has a basis to start (= it cannot turn Venus into a paradise or make Mars magically retain its atmosphere for 5 billion years).