How can I prepare for cycling 60 km, before getting the bike?

Edit: As discussed in the comments, I assume that OP is allowed to take a total of 2 hours of breaks, not that the ride (moving time) itself must be shorter than 2 hours. A 30km/h average speed over 60km would be challenging even for an experienced rider on good (but public) roads on a road bike.

It sounds like you are in quite a good shape. You should easily be able to do 60km in a day on a halfway decent bike. Unless there are lots of hills or headwind or bad roads. My sister recently got her first cheap 250€ city bike and imediately did a 90km trip along the Danube river without any issues. She didn’t do any bicycle specific training before but can probably perform all the exercises you mentioned.

Just take it easy, take a long break in the middle and remember to eat (but not too much and mostly carbohydrates, e.g. fruit or pasta or rice) and drink enough.

A wide saddle can chafe on the inside of your legs. A very soft saddle can put pressure on areas where you don’t want it. The specifics depend a lot on your body and your seating position. Just try the saddle which comes with the bike. Get bicycle shorts or at least tight shorts (e.g. running shorts) and wear them without underwear.

Adjust the saddle position to be high enough. As a rough estimate, with the pedal at the 6'o clock position and your heel placed on the pedal your leg should be fully extended. Considering your core strength you can probably lower the handlebars as low as possible for better aerodynamics.

You can’t really train endurance within 10 days. I’d take a few short rides (an hour or less) so your body gets used to the movement. Make sure your seating position is as good as possible and everything else is set up correctly (tire pressure, chain lube, shifting etc.) Don’t overdo it, you don’t want to start with sore muscles or a sore neck.

You can do so!

I had a 5 year long break from cycling. Then one day I decided I'll resume cycling.

On the first day of resuming cycling, I rode 2 kilometers.

On the second day, I rode 15 kilometers.

On the third day, I rode 22 kilometers.

Two weeks after starting riding, I rode 45 kilometers.

All of these kilometer numbers were from a bicycle that had no electric assist (today I also have an e-bike).

(To put things into context, before the break I did regular 50 km long rides nearly every day, and the longest daily ride I have done was 100 km. The 50 km long rides did not require carrying a water bottle with me or stopping for drinking or eating or any other reason for that matter, but the 100 km ride required stopping for drink and food.)

It did not take long after the break to be able to ride 30 kilometers. And I was in really bad shape, being overweight and not doing exercise often. A non-overweight person doing occasional exercise should be able to ride 60 kilometers 10 days after getting a bike.

The best saddle you can find is a plastic saddle that is fairly hard and narrow (but if you're a woman, you will want a very slightly wider saddle than the most typical narrow saddles, and there are of course some anatomical variations in men and women). Unlike leather saddles that are expensive, a plastic saddle is cheap. Unlike leather saddles that are destroyed in the rain, a plastic saddle is unaffected by rain. Unlike leather saddles that require lots of maintenance, a plastic saddle is zero-maintenance. Unlike leather saddles that have a break-in period, a plastic saddle requires no such breaking in.

Often it is asked why cyclists ride on hard and narrow saddles and not on soft and wide saddles -- wouldn't a soft and wide saddle be more comfortable? The reason is that to prevent sitting on the muscles that propel you forward, the saddle must be hard and narrow. Sitting on the muscles that propel the bicycle is not a good strategy on the long run.

When starting long-distance cycling or resuming long-distance cycling after a break, it hurts! The saddle feels really bad. This is why some cyclists want to buy a "better" saddle. The "better" saddle hurts too initially but because it wasn't free, the cyclist won't change the "better" saddle to the "best" (i.e. horrendously expensive) saddle.

Then eventually the cyclist notices the "better" saddle doesn't hurt so much anymore and becomes a fan of this "better" saddle, claiming it as a very comfortable saddle for a not-too-expensive price.

It wasn't the saddle.

It was becoming accustomed to riding on such a narrow and hard area. Most likely, the original saddle that was discarded would feel equally comfortable after a while.

Even though good (plastic) saddles do not require breaking in, the cyclist has a break-in period. Sitting on any reasonable saddle hurts a lot during the break-in period of the cyclist but stops hurting after the cyclist is fully broken-in.

If you stop cycling, the break in period starts again. So even a month without cycling means you have to break yourself in again. So, in areas that have a real winter, if you stop riding during the winter, your break-in period starts in the spring again.