As far as I could find the phrase brick and mortar meaning the provision of services in a building with human staff as opposed to computer-based service provision gained currency in the 1970s, mainly in the banking industry. Use of phrase in opposition to mail-order business appears to have started slightly later, even though mail order had been around for a long time. This Ngram shows brick-and-mortar branch and electronic bank taking off in the early 1970s (earlier instances of electronic bank refer to data banks); brick-and-mortar store does not take off before the mid 1990s. The earliest instance of brick-and-mortar in this modern sense I could find is from 1971, but applied to libraries though. And a charming thought it is:
Although claiming no gift of clairvoyance, I, too, can foresee a time when today's brick-and-mortar library will be obsolete. Our primary source of knowledge will be electronic information nodes or communications centers located in our homes, schools, and offices that are connected to international, national, regional, and local computer-based data networks.
Miller, Arthur R., “The Assault on Privacy: Information Technology―a Study of Good and Evil,” Law Quadrangle Notes, V. 15, Iss. 02 (Winter 1971) [full access]
Then, still in the realm of education, there is this one from 1974, or maybe later. When Google has several volumes or issues of a magazine together they give the date of the first issue.
[…] many courses, but not all, could be taught by a combination of two-way interactive instruction combined with extensive use of film and assisted, of course, by a computer terminal. There is no reason for a student to travel to a ‘brick and mortar’ type of institution to get this kind of instruction.
CIPS [Canadian Information Processing Society] Computer Magazine, vol. 5, issues 1-11, 1974, p. 96.
It was in the banking industry though that the phrase came to be more widely used. From the early 1970s banks started to offer banking services from ATMs and CBCTs (costumer-bank communication terminals) often away from their brick-and-mortar branches:
In November the Comptroller issued a new CBCT ruling, declaring that if CBCTs are branches, they differed from traditional brick-and-mortar branches and can meet less stringent establishment procedures,
Computer Law and Tax Report, vol. 2-7, 1975, p. 155. (computer “brick and mortar” 1970-80, #6)
The phrase pops up several times in U.S. Congressional hearings on the new electronic banking. This exchange took place in a hearing before the 94th Congress, so no later than 1976:
Mr. Bartell. Just on this point, though, are electronic terminals a substitute for or an alternative to brick and mortar branches? [p. 133]
Senator McIntyre. Dr. Mann, in Chicago we were told that electronic transfers were being widely accepted by the public at large, and they will make brick and mortar obsolete. [p. 400]
Federal branching policy: hearings before the Subcommittee on Financial Institutions of the Committee on Banking, Housing, and Urban Affairs, United States Senate, Ninety-fourth Congress, second session
Early in 1977 Toni Wiseman reported on further hearings in “EFT Unit Asks Limit on Federal Access,” Computerworld, Vol. XI, No. 9, February 28, 1977 [full access]:
Washington, D.C. ― Legislation should be enacted giving individuals the right to contest any government access to their financial information contained in electronic funds transfer (EFT) systems, according to an interim report released by the National Commission on EFT here last week. [p. 1]
The report recommended rules regarding the deployment of off-premise EFT terminals should be distinct from and less restrictive than those for "brick and mortar" branches. [p. 4]
Four years later, some people had grater expectations from e-business already. Here’s Desmond Smith, “Info City―New York Is Now the Information Capital of the World,” New York, February 9, 1981 [full access]:
A revolution is brewing in New York City: information is taking over. The revolutionaries are the people who have learned how to exploit the new micro-technology of computer-linked communications to the fullest: manufacturers who own no workshops, bankers who handle no cash, retailers who advertise goods “not available in any store,” and businessmen and women who “talk” to work rather than ride. (p. 24)
The electronic bank is replacing banking in the bricks and mortar sense everywhere, and it’s a lot cheaper to operate. (p. 26)
The earliest unambiguous instance I could find of brick and mortar as opposed to mail-order is from 1980 in Dun's Review (I checked here that the date is correct). There’s a possible instance from 1975, but I didn’t manage to check the context or the date itself. So it looks as though the phrase gained currency in the banking industry in opposition to computer-based service provision, and was then borrowed into the mail-order business context.
This idea that computer technology was going to reduce the need for brick-and-mortar was around in the 1960s already, but for a different reason: computer technology required less labour, and hence smaller facilities. So in the following quote brick-and-mortar is not used in the modern sense of alternative to e-business. But there is an opposition between computer-intensive and brick-and-mortar-intensive production systems that likely paved the way for the modern use of the phrase. The snippet Google shows is incomplete, so I combined it with the main output page. I checked here that a Univac III computer was delivered to Esquire Inc. in August 1963, so the Google date is correct: