LTspice XVII problem simulating SEPIC converter
You set the parallel resistance on the inductors to have the same value as the series resistance, which effectively fully dampens them (more like turning them into slightly inductive resistors). The parallel resistance should be at least k\$\Omega\$ in value, if not tens or more. If you remove those values, everything works.

Also, the parallel cap at the input does exactly nothing, unless you set Rser to the source, or cap, but then you can simply specify the source to be 7 Rser=10m Cpar=4.7u, and delete the cap.