How can you assign keys in tmux without Ctrl-b first?

tmux has several key-binding tables, as documented in man tmux under "bind-key". There are several default tables:

• The root table is where the prefix key itself is bound.
• The prefix table is used after the prefix is pressed, and is the one your usual keybindings go.
• The copy-mode table is used in copy mode if mode-keys is set to "emacs".
• The copy-mode-vi table is used in copy mode if mode-keys is set to "vi".

If you want to bind without the prefix key, use the -n or -T root option to bind-key.

Esc might behave slightly weird, as the terminal codes for nearly all special keys (Alt+keys, function keys, arrow keys, etc) also begin with exactly the same Esc. Programs like Vim use a timer to distinguish the two. You may need to lower the escape-time parameter in tmux.