Let's break it down by Fronts. Most missions, with the way they are structured, take less than a day (travel times not counted). Some Mission chains, mostly the FE's formerly known as weeklies take a bit longer.
Tutorial “Graduation Day” •
“Training Cruise” •
“Field Promotions” •
“Communication Breakdown” •
“Assimilation of the Innocent”
“Welcome to Earth Spacedock”
This basically happens all within a single day. Day 1 is Graduation, Trainings course, Borg Invasion, Field Promotion to Lt!
Klingon War “Stranded In Space” •
“Diplomatic Orders” •
“Hide and Seek” •
“Stop the Signal” •
“Researcher Rescue” •
“The Kuvah'Magh” •
“Treasure Trading Station” •
“Secret Orders” •
“Task Force Hippocrates” Let's be generous and call the Klingon Front so far 2 weeks. These are basically us patrolling the Klingon frontlines with back2back missions •
“Skirmish” •
“Spin the Wheel” •
“What Lies Beneath” •
“Everything Old is New” •
“Night of the Comet”
This basically covers about a month, though time travel shenanigans muddle it a bit.
•
“The Ultimate Klingon” •
“The Doomsday Device” •
“City on the Edge of Never” •
“Past Imperfect” •
“Temporal Ambassador” The rest of the Klingon Front might be another 2 weeks at the most.
So we are up to about 2 months total.
Wasteland “Secrets of Nimbus” •
“The Lost City of Paradise” •
“Blind Men Tell All Tales” •
“The Undying” •
“A Fistful of Gorn” •
“Installation 18”
If every mission on Nimbus takes about a day, this would be another week.
Romulan Mystery “Heading Out” •
“Under the Cover of Night” •
“Minefield” •
“Divide et Impera” •
“Saturday's Child” •
“Preemptive Strike” •
“Hunting the Hunters” •
“Project Nightingale” •
“By Any Means” •
“Ground Zero” •
“Ghost Ship” •
“Friend of My Enemy” •
“Taris” •
“Trapped” •
“S'harien's Swords”
Starfleet sends us to the Romulan front after the Tal Shiar Incident on Nimbus where we go back to patrolling with back2back missions. A month at the most.
We are at a bit over 3 months now in total.
•
“The Vault” •
“Mine Enemy” •
“Frozen” •
“Coliseum” •
“Cutting the Cord” •
“Darkness Before the Dawn” These were also weeklies, so let's say another month for this series. 4 months in total.
Cardassian Struggle “Venture into Deep Space” •
“Badlands” •
“Suspect” •
“War Games” •
“Shutdown” •
“Rapier” •
“Forging Bonds” •
“The Long Night” •
“The Tribble with Klingons” •
“Tear of the Prophets” •
“Crack in the Mirror” •
“The New Link” •
“Seeds of Dissent” •
“The Other Side” •
“Cage of Fire” •
“Second Wave” •
“Of Bajor” •
“Operation Gamma” •
“Facility 4028” •
“Boldly They Rode”
Including the Dominion FE, which is probably the most drawn out conflict of them all I would give the Cardassian Front 3 months at the most. Now we are at 7 months all in all.
Borg Advance “Report to Gamma Orionis” •
“Where Angels Fear to Tread” •
“A Gathering Darkness” •
“Assimilation” •
“Fluid Dynamics”
The newly revamped Borg/Undine Arc doesn't take more than a week.
Breen Invasion “Cold Call” •
“Out in the Cold” •
“Cold Comfort” •
“Cold Case” •
“Cold Storage” Another weekly series, so add another month. We are at 8.5 months roughly.
Solanae Dyson Sphere “Sphere of Influence” •
“Circles within Circles” •
“Supply Woes” •
“The Contested Zone” •
“The Omega Standoff” •
“Tower Control” •
“A Step Between Stars” •
“Fluidic Destruction”
These missions probably happen over a couple of months, since there is a lot of research and backstory happening with the 3 factions establishing a beach head in the sphere and all.
So at this point we need about 10-11 months for all major missions.
That leaves a couple of weeks for a Risa vacation and the short skirmishes and rescue operations we see in the queues. Basically the stuff that happens in between plus travel times which don't take that long with transwarp capabilities.
They couldn't have put much more into 2409 but it fits.
The only thing that strechtes credibility of course is the rise to admirality in that single year.
(except the special ones)
