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Although there are aero gains to be made on the frame, the main thing you are getting is a bike with geometry suited to a good position, that's where you gain the most.
That was my hope. I saw this offer https://www.ebay-kleinanzeigen.de/s-anzeige/zeitfahrrad-52er-rahmen/942258482-217-5903
As there is no description, except for the fact that the backwheel is not part of the deal, I hope the german language isn´t too much of burden.
I would sell nearly all the parts, but on an sq lab saddle, rival 1 x 11 and maybe some Aliexpress Carbon Bars and Stem.
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I think you might do well to have a look at this thread:
https://www.lfgss.com/conversations/144183/#comment6455026
I expect you know that many successful time triallists have come over from running, one excellent example is Alice Lethbridge who, among many other achievements, beat Beryl Burton's 12 hour record which had stood for half a century. So you are on a path which I hope will lead you to great things.
You don't give any indication of the level you hope to reach in your first season, and this is surely a relevant question when considering what kit is suitable.
Perhaps you are confident that you will quickly become a contender at national level, or possibly you are hoping to get a handicap award in a local club 25. If you're in the former category, I can't advise on equipment (too old fashioned), but if it's that handicap prize, then I can help.
It takes most people several seasons of racing to achieve their best, so there is a serious danger that if you start off with a super bike and then do beginner's performances you will be both disappointed and embarassed.
If you begin with a simple fixed TT bike (remember the name of this forum) you will be in a great tradition, have plenty of improvement to come and, with luck, you may even have bystanders saying "Look what he did on that old thing, we'll have to watch out if he gets a proper bike!"
Also, you won't have a large hole where your bank balance used to be.
As @Pifko said, even if it's not mine, I would go for a second hand frame and spend on wheels, skin suit and helmet.
Although there are aero gains to be made on the frame, the main thing you are getting is a bike with geometry suited to a good position, that's where you gain the most.