Fifteen Starship flights to fill up a fuel depot in LEO. 3-4 flights a month. And then you have to keep methane and oxygen cold for months. At 1 Solar luminosity.
A darkhorse alternative has been on various drawingboards for some time, as ToughSF notes: the tether. Looking around, a Tamil, name of Nagaraj Arjun Raja, suggests the Rotating Skyhook.
The idea is to get something to "space" but not yet to orbit. For orbit Raja expects 9.4 kilometers per second δV; BraveAI confirms this figure accounts for the 7.8 km/s orbital velocity needed to maintain orbit, plus 1.5–2.0 km/s lost to atmospheric drag and gravity drag during ascent
. I assume Raja assumes this to be launched from Sri Lanka so he's already using the equatorial surface daily velocity.
Raja notes that drag becomes negligible in the short term at 300 km altitude. We don't orbit sats there because sats are supposed to run for the long term. So if Raja's customers can just get something parabolic at apogee 300 km, Raja can catch it before drag and gravity matter. That δV is more like 7.
The skyhook's nexus orbits ~500 km going 7.612 km/s. The tether spins around such that, such that at 200 km below, the velocity is -3 km/s. That leaves 4.612 km/s to pick up the cargo. At the top of the tether, which is 800 km altitude, is +3 km/s. 10.612 km/s around that altitude is a trajectory to almost wherever you want, mate. Cargo will still need to correct that trajectory toward the mission parameter. Although that is Someone Else's Problem; Raja does suggest solutions to that Someone Else in section 7.
This costs up to 4.55 × 107 J per tonne, going back down to Earth; so 4.55 × 1010 J per kilotonne. Raja believes that can be countered with a honkin' magnet on the nexus, gradually pushing Earth's 25 μT at that altitude. The magnet is in part powered by the current along the tether, presumably conductive along with its other magic properties. That conductive (silver?) wire is not load-bearing; it's just along for the ride. Also various radiators and solar-panels can be attached to the nexus. The more massive the nexus, the less it dips down per cargo load. The skyhook can also catch cargo from outer orbits to bring them down to Earth-capture. That boosts the nexus' orbit for free.
Raja has one more contigency: an ion thruster running 1-5 kW delivering 3000 s of specific-impulse. Of course then you have to deliver ions.
The 200 km of cable can be Zylon worth 7-14 T. "Carbon nanotubes" are also on the table like they always are in articles like this, which would cut down a lot of this mass, if and when we can spin 200 km worth of it (hey at least it's not GEO-length). Likewise I'm not requesting anhydrous silica... yet. Raja is optimistic we can in fact get a good-enough CNT rope in 5-10 years, at the 13.8 GPa which competes with Jensen's anhydrous.
Zylon at this scale would be delivered by the Falcon Heavy. CNT, lighter for the requirements, could go to Rocket Lab. The overall timeframe is maybe 13 years from now.
As for section 7: that is where Raja suggests next-steps. One example is to put more tether-systems in higher orbits to catch and correct those Molniya orbits which the main tether will create. #7.3 handles trash removal. #7.4, most gonzo of all, would pick Mach 10-15 scramjet loads from the 30-50 km upper atmosphere. We would here need to dangle the rope so its velocity is -5 km/s (2.612 km/s in atmo). Drag would start getting serious so this length cannot be permanent. The cable dips down and pulls back I guess.