On my ATARI there was no DOS too. When you start the 65XE you can hold (iirc) START to start loading an application from the cassette recorder, but it was recommended to hold both (again iirc) START and OPTION to bypass BASIC, because BASIC interpreter being held in the memory, somehow interfered with bigger games (I think this was due to memory, but I'd like to learn from someone who know). I myself got into this trouble sometimes. Also you could have a CARTDRIGE with DOS-like Turbo management which allowed to scan cassette for given filename with binary application, but no one used this because it would take crazy long. I never had chance to use floppy disk, but I think it was behaving in a similar way (you had to have a floppy with DOS and hold START when powering the computer to load it), but at that time the FDD drives for atari were horryfyingly expensive (they had the same CPU 6502, and even there were some demoes which used this CPU as a coprocessor), so I stayed with a cassete reader with TURBO.

Of course games were also sold on CARTDRIGEs and this was the fastest way to play, but it wasn't popular in my country.

The original Atari 400/800 included BASIC on a ROM cartridge.

To use BASIC, you plugged the BASIC cartridge into the system and powered up.

To boot something else (games...., from either cassette or disk) you first removed the cartridge, then powered up.

With the XE series, BASIC was built in to the console, so the "magic keys" were needed to tell the hardware to virtually "unplug" the BASIC ROM before it tried booting from any connected devices.

Yes, Option would disable Basic on boot. The first Ataris (400 and 800) came with a basic module that you had to put in and then start the computer to use Basic - or likewise Assembler. The module would then use certain parts of the precious 64 KB Ram - actually, much less because the OS in ROM would write itself into RAM on startup and take about 20KB away. So a program or game had about 40 KB space to use. Basic would take some more away. Which wasn‘t a problem on the 800, you would either plug the module in and use Basic but you wouldn‘t if you wanted to load a game. But with the XL, you needed a way to disable the automatic Basic load at boot time, or many games could not use all of the memory they needed. Hence, the Option-option at startup.

At least I remember it this way, but I only had an XL, not the older ones, and now I remember that the 800 had only 48KB of RAM, so it was probably more complicated than that!