To be the first, you have to believe Babbage designed a general purpose computer that could accept instructions and never wrote any instructions.
https://www.bbvaopenmind.com/en/ada-lovelace-original-and-vi...
“I confirm that the manuscript evidence clearly shows that Babbage wrote ‘programs’ for his Analytical Engine in 1836-7 i.e. 6-7 years before the publication of Lovelace’s article in 1843. There are about 24 of such ‘programs’ and they have the identical features of the Lovelace’s famous ‘program’,” adds Swade. The historian says that the new tests are “unarguable” and that they “do not support, indeed they contradict the claim that Lovelace was the ‘first programmer’.”