Show Instantly taskbar when auto-hide on - windows 7

Follow these steps:

1. Go to My Computer;
2. Right click the My Computer icon;
3. Properties;
4. System properties;
5. Advanced;
6. Performance;
7. Settings;
8. Uncheck/check (as applicable) "Fade or slide menus into view";
9. Hit Apply and OK.

Alternatively on Windows 10:

1. Search for "View advanced system settings" in the Start or Settings menu.
2. Go to step 6 above.

As far as I know, the only way to speed up the process is to completely disable the Aero animations.

To do this:

1. Open your start-menu and type in "System" and select the option under the "Control Panel" section.
2. Click on "Advanced system settings" in the left-pane.
3. Click on the "Advanced" tab.
4. Click on "Settings" in the performance sub-section.
5. Uncheck "Animations in taskbar and Start Menu" and possibly (not sure if it is necessary) "Animate controls and elements inside windows".

Good luck!