You don't know anything about modern naval shipbuilding, then.
Allow me to point out to you that a “modern” navy was not required at Dunkirk. Likewise, the PT boats of WWII and the marine river craft of Vietnam were not very “modern”. Thousands of little craft carrying platoons across 110 miles is certainly very doable and actually very difficult to defend against if you do not control the air.
Combine that with a few larger naval craft, helicopters for both attack, rescue and transport and airplanes for paratroopers and amphibious assault, and you can build a LOW tech, high number reasonable chance of success in a short period of time. Remember, Victor/Liberty ships in WWII were being completed in 60 days.