I can't provide the most thorough answer as to whether something akin to a right to roam ever existed in the US, but American property law and the Constitution makes such a right hard to imagine ever having been formally recognized.

The classic case of Dougherty v. Stepp, 18 N.C. 371 (1835), involved a defendant who mistakenly thought that Dougherty's land was his and surveyed it, but didn't mark any trees or cut any bushes--i.e., there was no actual damage to the land itself. Dougherty sued for trespass. The North Carolina Supreme Court ruled in Dougherty's favor, holding that any intrusion on someone else's land constitutes a trespass even if no actual damage was done. The plaintiff may only be entitled to nominal damages (i.e., just a few bucks to legally recognize a legal harm was done), but the principle remains, and continues to be an axiomatic part of American property and tort law. Property rights include the right to exclude, at least in this country.

Another difficulty in creating an American "right to roam" is the 5th Amendment's Takings Clause, which prohibits the taking of private land for public use without just compensation (this is the so-called "eminent domain" power of the federal government--they can, in fact, take your land, they just have to pay you for it). The right to exclude is so fundamentally a part of American property law that a statute allowing the public to roam on private lands would almost certainly face a serious, probably fatal, 5th Amendment challenge from property owners.

However, that doesn't mean there are no equivalents to the right to roam in some limited circumstances. Some states have a default rule allowing access to private land (or, more accurately, imposing no penalties) if the landowner does not post no-trespassing signs or otherwise indicate the land is private property. Others provide public access to some parts of the seashore--typically property held below the mean-water line. Some (but not all) parts of federally held public land and national parks are also accessible to the public.

Furthermore, just because trespass law technically existed somewhere hidden in the annals of a courthouse doesn't mean these laws were enforced systematically. It's hard to imagine that people didn't trespass on each others' land all the time in an era where posting and fencing was not as thorough as it is today.

And this isn't really a "right to roam," but the Supreme Court has long held that there is a right to interstate travel (i.e., to travel freely between the states) in the Constitution. This right was included in the Articles of Confederation but was considered so obvious that no one seemed to bother putting it in the actual Constitution a few years later. The case Crandall v. Nevada, 73 U.S. 35 (1868) formally recognized the right to interstate travel in a case wherein Nevada tried to tax people leaving the state. The tax was struck down as a violation of this fundamental right to interstate travel (despite, again, such a right not actually existing in the text of the Constitution).

One thing to keep in mind is that property law and tort law (the two bodies of law most relevant to trespass) would likely not have been codified by state or colonial legislatures in any thorough way. The United States, both before and after independence, used (and uses) a common law system, in which judges make a great deal of law through their written opinions. If you try to go looking for actual statutes on trespass before the 20th century, you'll probably have trouble finding many.

Sources:

Jess Kyle, Of Constitutions and Cultures: The British Right to Roam and American Property Law, 44 Environmental Law Reporter 10898 (2014)

Jonathan Klick & Gideon Parchomovsky, Roam If You Want to, 40 REGULATION 18 (2017).

Dougherty v. Stepp, 18 N.C. 371 (1835)

Crandall v. Nevada, 73 U.S. 35 (1868)

U.S. Constitution

EDIT: accidentally switched the parties in Dougherty v. Stepp. Sorry!