the LDS church became the first institutional sponsor of the BSA >>>
wasn’t the YMCA the first?
You may be right.
If there's a doubt or an ambiguity, then I'll bet both claim to be the first. What I've read lists LDS.
There's also the possibility that YMCA can make the claim because it sponsored BSA Scouting, while the LDS struck a deal to have a distinct Scouting program called "LDS Scouting."
It's not unusual to have different Scouting programs in a country; most European countries have several different Scouting organizations based on religion, labor unions, or distinct area of the country.