Quick route from Cinque Terre to Burgundy

I'm not the expert on train travel here, but since no one else has answered here's the best I can do - others will probably improve on it. I think you start by exiting CT toward Genoa, catch a train to Milan, then another to Dijon. Genoa to Milan is about 1 1/2 hours by train. Milan to Dijon is about seven hours. Be sure to consider time to Genoa and connection times when you plan the trip. The local train through CT runs regularly but I'm not sure it runs all night. Time of year may also matter. We visited in October (from La Spezia) and I think the CT train ran hourly - it may run more often in summer months.

You might also look at La Spezia-Milan-Dijon. Nothing is going to be "quick".

What about the coastal train once in Genoa, that goes to the French border. From the French/Italian border it's three hours to Marseille and then transfer to a TGV that goes up to Dijon.

Thanks so much. That may be the quickest route rather than going through mountainous regions.