The only way to make a multiline cursor in Sublime text 3 is Ctrl+Shift+RC+Drag. Is there any way to do this without using a mouse?
Yes, there is. Using Shift↓ or Shift↑, select the lines you want multiple cursors on. Next, hit CtrlShiftL (CommandShiftL on macOS) to split the selection into lines. Finally, hitting ← will put the cursors at the beginning of the lines, while → will put them at the end.
Edit
There is also another, quicker way (thanks to minitech) - CtrlAlt↑/↓ will create multiple cursors without having to do selections first, and you can place the cursors anywhere in the line you wish. However, on Windows these key combos may be mapped to changing the screen orientation. To change this, hit CtrlAltF12 to open the Intel control panel, click Options
, and either remap the screen orientation hotkeys, or click Off
on the left side to disable all of them.