bought 2024 MacBook m3 chip Arm Architecture and I'm trying to install Arch Linux

On the Arch Linux | ARM site, I don't see any mention of Apple Silicon Macs as supported platforms.

https://archlinuxarm.org/wiki/Platforms

There are several ARM-based distributions of Linux that will run in a Parallels Desktop ARM virtual machine. If you are just interested in playing with Linux as a user, it might be easier to run one of them, than to try to get the Arch Linux / ARM distribution to work on a Mac. That might be a low-level operating system driver porting project.

Asahi Linux is furthest along with Apple silicon Arm AArch64 support, and they are remixing their changes into Fedora.

How long before that filters into Arch, and preferably without particular added architecture-related effort throughout? Likely nobody around here knows that.

For the near- to mid-term, if Arch is your goal, and if native x86-64 performance your preference, then an Intel PC is a better choice. Pending that, you might be best served with macOS and a virtual machine, and Arch booted as a guest either virtualized, or virtualized and emulated (e.g. UTM), as mentioned above.

According to the FAQ, the official distribution of Arch Linux does not support ARM CPUs. That distribution only supports the x86_64 architecture. There is an unofficial port for ARM CPUs, with its own community channel.

https://wiki.archlinux.org/title/Frequently_asked_questions

UTM can allow you to run an Intel version of an OS on an M-series Mac, but performance will be impacted since UTM emulates a computer with a particular CPU architecture as well as provides virtualization.

You may be able to run ARM versions of Linux within a Parallels VM (paid third party app).

FYI, I know you did not mention running Linux on bare metal which is good since I do not recommend running Linux on bare metal on the M-series Macs for multiple reasons. One, M3 support is still rudimentary and even M1/M2 support still has lots of issues. Plus, many people seem to need to perform a clean install of macOS which involves first erasing the disk (best to perform a DFU firmware Restore in that circumstance) in order to remove a bare metal installation of Linux even when installed to an external drive since the internal SSD must be modified as well even for an external Linux installation on bare metal. I do know the instructions for uninstalling/removing a bare metal Linux installation is hard to find and tends to have very little information.

Running a non-Apple OS in a VM or possibly using UTM is the best option on an M-series Mac at this time. Using an older Mac or a dedicated non-Apple PC may give better results since almost any Intel/AMD 64bit PC with a decent CPU (forget cheap low end PCs) which will run Linux on bare metal.