Green’s Dictionary of Slang

by sheer luck.

1930		D. Hammett Maltese Falcon (1965) 332: You’ve got to convince me that [...] you’re not simply fiddling around by guess and by God, hoping it’ll come out somehow all right in the end’.
1943		Reader’s Digest Oct. 79: No more job training ‘by guess and by God’ [DA].
1953		Randolph & Wilson Down in the Holler 232: by guess and by God: phr. More or less at random, without any accurate measurement.
1974		in Sports Illus. 15 Apr. in Davis (ed) Permanent Wave 221: ‘I can’t say I’m an expert whitewater canoeist. It’s by guess and by God with me’.

taking a course of action or movement without any real plan.

1909

J.C. Lincoln Keziah Coffin vii 104: If ever a craft was steered by guess and by godfrey, ’twas that old hooker of Zach’s t’other night [DA].

(US) haphazardly, without a planned direction, at random.

[1888		Journal of Outdoor Life (N.Y.) 15 Nov. 335: The forms in use are the birch and primitive log pirogue, with a few lapstreaks of uncertain shape and unknown weight, and for the most part built ‘by guess and by greenness’].
1891		Journal of Outdoor Life (N.Y.) 17 Sept. 175: The course was triangular, 3 miles on a side, twice around; but no the buoys were set ‘by guess and by jingo’ by an old fisherman, the course was not more than 14 miles all told.
1896		N.Y. Times 12 Jan. 27: Now, I don’t propose to run my oyster cooking by guess and by gosh, but I have a thermometer and require the fat to be heated to a certain temperature.
1914		J.C. Ruppenthal ‘A Word-List From Kansas’ in DN IV:ii 104: by guess and by golly, prep. phr. Hit or miss. ‘I didn’t have anything to go by. I just did it by guess and by golly’.
1947		National Geographic Mag. Sept. 326/2: The long sand trail needs one who can drive by guess and by gosh and feel cheerful in the midst of seeming chaos [DA].
1972		(con. 1916) G. Swarthout Tin Lizzie Troop (1978) 113: Don’t go by guess and by gosh, get to know ’er inside out.