I agree with the Hemmets card as the first one I know of, and certainly the 1962 Rekord, which is clearly meant to be cut out as a strip-type card, as the next.
Murr raises a very good point, one that I am going to address at length in an upcoming entry on my web site 'soapbox': owing to the nature of boxing promotions, the first 'card' you are likely to find for many boxers is a self-issued publicity card. They were standard items from the 1920s through the 1950s-1960s and can often be dated based on the fighters' attributes and date stamps from newspaper archives where many of them were saved. Here is my Clay with the letter enclosing it, from before the first Liston fight:
Other examples:
Pre-championship Rocky Graziano:
1953 Floyd Patterson:
Early 'Two-Ton' Tony Galento; looks like he was half a ton short here:
The Cocoa Kid; try finding another card of this HOFer:
A very young Max Schmeling:
Some call these photos, some treat them as cards. Where the line is between items like these and 'photos' like the ACC-listed H815 Adam Hats 'cards'?
There is also Clay's Exhibit card, which is an early 1960s issue:
I could pin down the exact issue date for certain if I had an Exhibit catalog collection from the era, but I don't. Some collectors toss out all Exhibit cards and all postcards too. Fine by me--collect what you want--but don't tell me that Gene Tunney's RC is anything issued after his 1922, nationally-distributed, American-made Exhibit card:
My point being that if you toss out this item and that item and that item and those items you can skew your analysis pretty much to any outcome you wish to justify anything you want to treat as the card as being THE card. I mean, even starting from the OP list of cards, technically, none of them are classic RCs. Beckett--which started the rookie card stuff in the 1980s in its books and mags--listed any foreign-issued card not available as issued in the USA as an XRC, so every one of the cards listed in the OP are not really 'rookie cards' under the classic definition, they are XRCs. If you want to admit foreign cards into the rookie card mix, you are already discarding the classic rookie card definition and substituting one that is not generally accepted. Again, I have no issue with that per se, but stating this card or that card is the definitive first card for a fighter requires rigorous intellectual honesty in the analysis, first to define what a card is then to define what it means to be a rookie card, and lastly to divorce the decision from parochial considerations, like glossing what you own and would like to tout as the key card. Unfortunately, those subjects are not at all clear, especially where issues from everywhere on the planet are considered. I find the 'rookie' designation increasingly problematic the wider the net is cast. I mean, can a local card issued in Spain or Sweden that literally no one collected be considered a 'better' card than one issued in the USA or Great Britain?
See what I'm getting at?