How did Woz write the Apple 1 BASIC before building the computer?

What Woz did was the default way of writing assembly language programs for owners of 8-bit computers (mostly hobbyists). You didn't have money for a second machine, so you wrote your program on paper, you entered it then tested it in situ. Mostly you got it right, as doing it on paper was slow and meant you had the opportunity to put lots of thought into it. 8-bit instruction sets were simple enough that you eventually learned the most common instructions by heart. There was a point where I could mostly translate a Z80 program from assembly to machine code from (my) memory.

Maybe that is part of the nostalgia for the 8-bit days: the practice of "slow programming"? It was relaxing, sort of like those "slow tv" shows.

I would say bit by bit, I mean "small part" and then keep making small extensions to the program(s)

First for new hardware would be a monitor program. Either write one, or port one from other hardware. A monitor program allows the inspection and edit of memory data and also to run programs in such memory. The monitor program often placed in ROM for convenance. A 6502 cross assembler, could be used to avoid the need for hand assembly the program to 6502 machine code.

Probably where WOZMON came from.

Then using WOZMON start writing a VERY simple basic interpreter.

It's taken me more than 40 years to learn a fraction of a % of what Woz knew in 1975.

For the sequel to this, see:

https://www.folklore.org/MacBasic.html

I only had to assemble instructions by hand three times in my career. It is not difficult if you are already familiar with the ISA of that particular processor, but it is tedious.

The first time was in my first job writing OpenGL ES 2.0 blending operations for the Imagination Technologies SGX 535, which was a remarkably advanced little GPU for its time. Alpha blending happened through special instructions in the fragment/pixel shader. We did have a compiler, but it didn't handle blending, for whatever reason.

Through testing I noticed that NVidia GPUs performed blending incorrectly, according to the specification, which was a big surprise. Only years later I figured out that the specification had some errors; I now would bet that NVidia was doing the correct thing.

The second time I had to assemble instructions by hand happened while working on a stripped down version of the Radeon 7xxx series that shipped on some mobile phones. I don't recall what the problem was, whether we were adding a feature or optimizing the microcode generated for a particular OpenGL operation, but it involved a rarely-used feature called user-defined clipping planes. We didn't have an assembler for that GPU; all microcode was assembled by hand.

The third time happened at NVidia, and I will be vague, as not enough time has passed for me to be comfortable going into any detail. I had an idea for how to provide hardware acceleration for persistent CUDA kernels, which eventually was marketed as Cluster Launch Control (CLC). In order to quantify the benefit of adding some hardware, when it was possible to approximate that functionality in software, I needed to test the most efficient software implementation that was possible, and the compiler wasn't quite giving the assembly I wanted, so I had to manually patch some instructions post-compilation. Why did I not use the assembler that was available? I couldn't, because the assembly language did not provide a way to express the exact feature I had to patch.