The short answer
Not in the modern sense. He wanted monopolies, bounties and prohibitions swept away. He also gave the state three duties, the third of them large, and he was explicit about how it should be paid for.
The three duties
Remove every system of preference and restraint, he wrote, and the sovereign has only three duties left. The first is defence. The second is justice. The third is erecting and maintaining certain public works, and certain public institutions that no individual could ever make pay, though they may be worth far more than they cost to a great society.
Under that heading he put roads, bridges, harbours, canals, the coinage, the post office and schools, paid for, wherever it could be managed, by the people who used them.
Schools, banks and taxes
The division of labour that opens the book, he wrote near its end, can make a worker as stupid and ignorant as it is possible for a human creature to become, unless government takes some pains to prevent it. His remedy was public education, paid for partly from public funds.
Banks had to be restrained, for the same reason a party wall is required between houses: one man's fire can burn the street.
Taxes should fall in proportion to income, and he thought it not very unreasonable that the rich should contribute something more than in that proportion.
Where the small-government Smith came from
The minimal-state Smith was assembled after his death, and it was taken apart from inside the University of Chicago by the economist Jacob Viner as early as 1927. The people best placed to know were saying so in print half a century before Smith became a symbol on a necktie.