There are only two ways of producing "value". You either extract resources from the planet or you use labor to enhance those resources. The value is in the problems solved by the finished product.

Capitalism requires that capital is invested in the manner which produces the most profit. Thus infinite growth.

There is not an infinite amount of resources or labor. The fruit tree extracts nutrients from the soil and requires water to be added.

I know at one time there were zero bikes, now there are more than zero, and I suspect more will be created...

Correct but, there cannot always be more bikes... At some point there may not be demand for more, or materials run out or become too expensive... Taken to the extreme, you cannot produce more bikes forever

For discussion, perhaps it would be easier to reduce the complexity. In a capitalist system, if I own a fruit tree in an ideal climate then not only can it be duplicated, but either it will produce value by itself, or I will by picking its fruit.

Again, globally we may produce x billion tons of fruit this year.... Maybe a few million more next year... Can we always produce more fruit (more as in a greater number than last year) forever?

Think longer term. Let’s go with that Fruit analogy. If you have a fruit tree in ideal conditions and begin growing more, eventually you will hit conditions that are not ideal. You can make them more ideal, you can buy more land that is ideal with the fruit proceeds. But eventually you will run out of land where it is possible to grow fruit trees. The supply is now limited. But before that, you will hit a point where people no longer demand the fruit, and your fruit is not worth the upkeep of your orchards.

So you increase the price to try and reach parity before you farm all the land, and you keep a store back for droughts and other problem periods. (Companies like DeBeers store back diamonds to hit this point artificially without risking a drop in demand)

Now imagine every person is trying to grow as many fruit trees as possible. That land runs out a lot faster and the saturation point is reached faster. The point where it makes sense to grow more trees is hit a lot sooner.

Advertising is another form of artificially raising demand. If you think you are hitting an equilibrium you have to start trying to convince people that your product is special and better than the other guy’s product.

Ultimately, the system is finite because land is finite, demand is finite, and people are finite. You can’t expect eternal growth in a finite system.