SEI
Nope and just nope!
400BN$ stuff is sooo misinterpreted. In 1989. Bush Sr. announced the Space Exploration Initiative. NASA did a 90 day study, called "90 day study"
They gave Bush a program costing a bit over 400BN$. It included:
Large scale planetary probes for study of Moon and Mars in preparation for manned exploration. Space station Freedom, in its dual keel configuration in which it could be used to assemble and maintain Moon/Mars transfer vehicles. Orbital transfer vehicle used to ferry modules and cargo from LEO to GEO and to the Moon. A GEO manned station.
A improved space shuttle. And unmanned transport Shuttle C. And two new non reusable heavy lift booster to be used to launch Moon base and Mars ship components.
A series of Manned flights to the Moon, starting around 2002/3 and construction of a Moon base. Assembly of first Mars bound ships around 2015-2020 and subsequent first manned mission to Mars. And several following Mars expeditions of such type. Culminating with a non permanently manned Mars outpost around 2030.
All that, over almost 40 years, was estimated to cost ~400BN$ with a large reserve included in the number.
News reporters quickly rounded the number to 500BN$ and said that would be the price of a single Mars flight. In following years since, in its NASA bashing use in press, that numbers has been enlarged by inflation, and a arbitrary additional enlargement of price on the bias and opinion of the reporter witting the text.
Now, about the any possible mission. Yes the recycling systems we have or will have are nowhere near needed. So you just use a ship assembled in orbit over a year or two (so you have a start mass around 500 tons), you have a crew or 3-4, and you basically carry all food and watter you will need on the journey. Water and air recycling will be needed to be recycled as good as technology provides. Food you simply have to carry with you. You put crew area to be surrounded with watter tanks (and possibly fuel tanks) so they can act as radiation shield. And you carry only one really good shielded compartment to serve as storm shelter in case of CMEs and other solar flares.
Now, over 1969-1971 US launched how many? 7 Saturns V? Thats around 800 tons in LEO. If you launch food, watter and fuel last, you don't have to worry about shelf time and fuel evaporation, so assembly well can take 3 years or more.
If you use Venus for a slingshot, you need to go in ~1980. If you develop a nuclear engine you could go any two years, but time to develop them will prolong the project, and increase expenses. And developing a lander will take time. But its just a engineering challenge, therefore solvable with right amounts of time and money.
If you are deciding on a plan in 1969. you could cut Appolo at 14 or 15, and build additional 3-5 Saturns V and have a launch vehicle for a 600 ton Mars ship.