That’s a great question. Let’s take a look! It’s in a book! (Okay, actually it’s on Wikipedia, but still…)
So, the usual procedure here is that the local government pledges the funding necessary to build a stadium, then MLS awards a franchise very soon thereafter, and then shovels hit the dirt. To wit:
Austin is getting a franchise beginning play in 2021. The owner of the Columbus Crew announced his intention to move that franchise to Austin in October 2017. On Dec. 19, 2018, the ownership group and the city of Austin reached a financing agreement for a new soccer-specific stadium. On Jan. 15, 2019, Austin was awarded an MLS expansion franchise. (The Crew will remain in Columbus under new ownership.)
Nashville is getting a franchise beginning play next season. Nashville’s ownership group launched a franchise bid in August 2016. On Nov. 6, 2017, the city council approved a $275 million stadium project. Nashville was awarded an MLS franchise on Dec. 20, 2017.
Miami is also getting a franchise next season. Now this one is a special case because David Beckham was given the opportunity to purchase an expansion team for $25 million as part of his contract when he joined MLS as a player in 2007. In 2014, he exercised that option, and the bid spent four years in development hell, with MLS commissioner saying repeatedly that the expansion would not be approved until a downtown stadium plan was secured. I’m guessing MLS’s lawyers didn’t write that requirement into the contract, though, because Beckham was finally awarded a franchise in January 2018. Ultimately they did get public financing for the stadium approved later that year, although it’s still not clear it’s ever going to get built.
Cincinnati has a brand new MLS team that started play this season. That ownership group had been negotiating with MLS for a franchise since 2016. On May 16, 2018, the city council voted to build a new $200 million stadium with public money. MLS awarded Cincinnati a franchise on May 29, 2018. What’s especially interesting about this case is that Cincinnati had a franchise playing in the USL that was already drawing more than 20,000 fans per game to play in a perfectly good stadium the team shared with the University of Cincinnati’s college football team, but MLS was absolutely, positively adamant that Cincinnati was not getting a franchise until the city ponied up to pay for the construction of a brand new soccer-specific stadium.
Admittedly, MLS has been sometimes willing to make exceptions for mega-mega markets like New York City, Los Angeles, and Atlanta. But everybody else, you get a stadium deal firmly in place, and then MLS awards you a franchise a couple of weeks later.