I would do:
```
inoremap <Tab> <Esc>/[\])}$]<CR>a
```
This mapping:
- Switch to Normal mode `<Esc>`
- Search for a closing brace (`)`, `}`, `]`) or a `$` `/[\])}$]`
- Switch back to insert mode `a`

But it is not exactly the same of going one level up in nesting.

If you activate the builtin `matchit` plugin (`runtime macros/matchit.vim`) you could do:
```
imap <Tab> <Esc>]%a
```

It uses the `]%` which is the equivalent of `])` but for all the 'braces' considered by matchit.

Remark: It doesn't support `$` because for `$` the open and closing brace characters are the same which make determining the level of nesting much more complex.