Is there a feasible way to create a large number of long random DNA strands?
Chemical DNA synthesis has you covered for short DNA strands.

It's possible to just use an equimolar mixture of all 4 bases when you do chemical synthesis, which results in random sequences. (This is most often used to generate barcoded primers).
The main problem with this approach is that:


chemical synthesis is not super efficient, anything above ~1-2kb will likely not be possible
If you work with a fully randomised sequence it becomes much harder to do quality control of the product (you can't sequence it).


You can also easily even calculate the probability of generating all possible sequences for a given strand length and yield.