I have tried different things in different languages for a couple of years and in everything I do, you need to download a multitude of different softwares that enable you to begin programming. Such as libraries, compilers, addons ect. Is it possible to open up notepad, program a compiler for c++ and then work your way from there? Or is downloading software absolutely necessary?
You don't need (in principle) to download programs to learn programming. I started to code in 1974, before Internet was available.
You program by writing source code in some programming language. Your source code needs to be handled by some program, which is either a compiler or an interpreter. And you need something to give you the ability of typing source code (an operating system with a file system, a source code editor, a file manager, ....).
That compiler or interpreter should exist on your computer (and you also need some operating system in practice).
You could buy a computer with an operating system, a compiler (or many of them) and/or an interpreter installed on it (your vendor would probably do the downloading and installation, and you'll pay him for that work). For example, many Linux distributions have all that (and I recommend using Linux to learn programming, it is very student- and developer- friendly).
For commercial reasons, Windows is not installed with all these.
In practice, you need many other programs to write code comfortably (source code editors, version control systems, command line interpreters, linkers, debuggers, build automation tools, various software utilities).
you need to download a multitude of different softwares that enable you to begin programming.
Some programming environment are more friendly ; e.g. DrRacket is probably packaging several tools together.
If you code in C++, don't confuse the IDE you are using with your C++ compiler. Your IDE is likely to run a compiler (e.g. GCC) for you behind your back, and you'll better be able to run your C++ compiler on the command line. You generally want to enable all warnings and debug info, so with GCC you'll compile with g++ -Wall -Wextra -g.
Is it possible to open up notepad,
Better learn to use a good, real, source code editor such as GNU emacs (it is free software). If coding in C++, you want syntax highlighting, automatic indentation and prettyprinting, autocompletion, brace matching, etc.... and you'll configure your editor to suit your needs.
program a compiler for c++
Wrong terminology. You don't program a compiler, you just use an existing C++ one. In practice, C and C++ compilers are very complex pieces of software (because they are optimizing compilers), of many millions lines of source code. Both GCC and Clang/LLVM are free software C++ compilers (coded in C++ so bootstrapped); you can download their source code and study and improve it (you'll need years of work for that).