I've always considered Fortran to be the "first", but with some quick research, it looks like Algol was the first C-like lang to add an if/then statement. My guess is that the author was trying to approximate modern imperative programming.
Fortran was the first compiled language, that is, the first language at a level higher than assembler. But Algol was a block-structured language in a way that Fortran wasn't, and virtually all languages of that "group" are block-structured today ("goto considered harmful" and all that). So Algol is more appropriate as the "prototype" of what exists today.
Mercury Autocode is perhaps a "missing link" between assembler and Fortran, though I'm not sure of the dates and whether the people developing Fortran knew about Mercury Autocode. Things developed quite fast in the 1950s.
[1] https://craftofcoding.wordpress.com/2021/01/11/why-algol-bes...