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I have a sink base kitchen cabinet going in the basement. I have cut
up some 1/4" thick plywood to put on the sides and toekick. Its
particleboard from the factory. Problem is how to glue it to the
cabinet. Festool rail guided circular saw worked wonders cutting the
plywood.

Option 1: Use yellow woodworking glue. Problem is getting pressure
on the plywood. Sink base sides are 34" x 23". Sink base is 5 feet
wide. So I do not have long enough clamps to use cauls. I've thought
about putting bags of cat litter on top of the plywood to weight it
down. 200 pounds or so. Not sure it will be enough pounds per square
inch of pressure. The plywood is also not perfectly flat. It has
some waves and twists and bows in it.

Option 2. Contact adhesive. I think it will work with plywood as
well as it does with plastic laminate.

I have added lots of short but wide 1/4" bead board panels to all of the
walls in our bathroom. Typically they were 30 inches tall. I used
construction adhesive specifically intended for the use of installing
paneling w/o nails. Read the instructions as IIRC you apply the adhesive,
set the panel in place for a few moments and then remove for a predetermined
period of time, and then reapply the panel. Still working in 6 years later.