Glue-Down Engineered Hardwood New Installation - Gap Size b/w Floor Edge and Baseboard

Was there carpet before?

From my un-expert opinion, whether acceptable or not, it's what you have now.

Of course, you could argue, and perhaps eventually get your installer to uninstall, buy new material, and reinstall,

or, use a larger piece of shoe mold?

It does seem like the installer should have looked at the existing shoe mold, and made sure it covered his gap.

Maybe a solution is Him purchasing and installing larger shoe mold?

Sounds like a sucky situation. Best of luck.

Edit to add: Caulk the few gaps? Add flooring material to the few gaps?

When we laid glue down wood we would gap it around 1/4". Sometimes we'd put wood shims in between the wood floors and base and just bump them to the shims then pull them out when the floors dried.

1/2" is too much. Definitely doesn't need to be wider than what your shoe mold would cover. Any flooring guy should know that.

As much as I hate to see quarter round on a flooring job, this is regrettably your best option. Quarter round is usually 3/4” x 3/4”. Shoe molding is 1/2” x 3/4”. This is a much better look. Whenever I see quarter round used instead of shoe molding I immediately know the installers were not knowledgeable.
Like the above poster said, ther should be 1/4” gap between flooring and a change of plane.