Hello
It appears your assessment is correct - there is generally only 1 direct Intercity train from Ventimiglia to Sestri Levante a day and it is really early so I doubt it will work for you to catch it. Considering that you are technically crossing 2 international borders and changing train systems at least one of the changes is pretty much unavoidable.
On a random weekday morning even Google is hedging on how long it will take "2 hr 50 min to 4 hr 10 min" and I'm sure the 3 +/- and hour range is coastal traffic uncertainty.
I have driven in Nice off-season and I cannot imagine wanting to sign up for that again when the train is a viable option. Driving cross multiple countries and hassling with a rental car compared to sitting on the train and watching the endless views of the Mediterranean roll past even with two changes? I know which I would choose even if it adds an hour or two to the travel.
My $.02, have a great trip,
=Tod