Still a healthy dose of ambition
At its peak, Atlas V flew about once per month. The gap between the last two launches was 11 months so there has been plenty of room in the schedule for Kuiper but no launches. The reason for that is Amazon did not want to waste a powerful Atlas V launching just two experimental satellites. Assume the first Atlas V launch goes this month. There will be some delay while the satellites get tested, with the possibility of some more delay if those tests show a need to re-work the current inventory. Once Amazon have confidence in their satellites the remaining Atlas launches should easily launch in the time available - but there are only 9. ULA stopped building Atlas cores to coincide with the end of their stock of Russian made engines. In theory Amazon could pay to get Vulcan human rated to free up some Atlases reserved for Starliner. Cue complaints from Amazon shareholders and NASA.
Falcon 9 launched twice in its first year (2010), zero times the following year and did not break 10 launches per year until 2017 - coinciding with the first booster two fly twice. Although this was a different era for launch demand, SpaceX was famous for their long waiting list. Most of the delays came from ramping up production and learning how to quickly cycle the ground support equipment. RocketLab currently launch about once per month but that involved considerable time switching from hand made by rocket scientists to mass production by trainees. A part of their rapid growth was launching from New Zealand. Falcon gets to launch so often because they now get a very narrow launch corridor with minimal disruption to congested Florida airspace.
Blue Origin are just starting their transition to engine mass production, with a much more difficult engine than the electrically pumped Rutherford or even Merlin - which benefited from years of research into simplifying manufacture. Vulcan is going to start with a shortage of engines and if that gets fixed will smack into trying to get frequent licenses to launch an experimental rocket into congested airspace.
Ariane 5 maxed out at seven launches per year. Kuiper has 18 Ariane 6 launches booked. Like Atlas and Vulcan, these are expected to bare the brunt of the early launches while New Glenn gets started. Ariane is building up a backlog of other commitments (like Vulcan) so will have to start their cadence at a sprint to meet the deadline.
The plan for New Glenn is to land successfully on the first attempt. By itself that is ambitious. It took SpaceX a year to re-qualify a used Falcon 9, and that was with a rocket that had been flying for six years. New Glenn also has to start at a sprint. The cores are not as easy to build as Falcons so if one gets dented it will hurt the schedule.
Amazon could still meet their deadline with their existing plan but that requires everything else to go smoothly with a new satellite, three new rockets, two new engines and first time re-use.