Would the Federation still have gone to war with the Klingons knowing there was a bigger threat out there somewhere? Georgiou wouldn't have died on the Shenzhen? Burnham would've been a decorated, respected officer without going the mutineer route? The MU incursion would never have occurred, and Lorca would still be in command of the Discovery?
Would the spore drive have been weaponized?
They'd start with a flashback to the death of Burnham's parents, her getting rescued by Starfleet Officers, then showing her joining Starfleet Academy when she grows up. This is where she'd meet Tilly and Saru. After that, they'd have her take the Kobayashi Maru test. Then she'd graduate and be assigned to Discovery, along with Tilly and Saru. They still fight the Klingons but, over the course of this, Burnham somehow becomes First Officer. After Georgiou dies fighting the Klingons, Discovery retreats. Burnham is promoted to Captain. She makes Saru her First Officer. This is the Kelvin Timeline, don't ask. Just go with it.
They have to figure out how to fight the Klingons. Enter Stamets, who has an idea for a Spore Drive. They want to add to the Spore Drive to Discovery. Then they hear about the Klingons attacking an outpost and only Discovery can get there, if they install the Spore Drive. They get it installed in the nick of time, then they Spore Jump to the world the Klingons are attacking, make their big splash, and Discovery wins against them, making a name for itself.
The Klingons don't like this and go after Burnham. There's a huge battle, this is the one that could decide The War. Burnham has Stamets do 133 jumps. They beat the Klingons. They're about to head home, then there's an energy disturbance, and then they end up 930 years in The Future.
So no Lorca, no Mirror Universe, no Pike, no Shenzhou, and they just skip from one thing to the other. The only Klingons we see in this super-shortened version are T'Kuvma and then Kol. No L'Rell or Voq. In turn, no Tyler. The story for Season 2 is skipped completely. Pike is dead (since
Star Trek Into Darkness would've already come out) and Spock would be doing his thing on the Enterprise-A with Kirk.
No relationship between Stamets and Culber either. At most, Stamets hugs Culber in such a way that it looks like it could be a bear hug for two seconds (can't have it looking
too romantic since there's no way Culber could pass for a family member) before Culber gets killed when the Klingons attack. So you
could say they
might've been in a relationship but, for the homophobic, you could also say they were just "best buds".
I like the real
Discovery better than this Kelvin-ized version.