NEW YORK — The city has become an archaeological site, with thousands of artifacts such as an 18th-century bone toothbrush with animal hair bristles and wine and champagne bottles corked centuries ago unearthed to prove it.

A copper half-penny and a pair of children’s shoes are some of the other remnants of early New York life workers discovered in lower Manhattan while digging to install new utilities for the growing residential and business South Street Seaport area....