Is there a tankless water heater with instant hot water?
The tank is not the issue.  The distance and pipe size is the issue. 

There is a considerable length of "hot water" pipe between your hot water heater and your shower or sink. That pipe is always full of water.   Over time, this water cools off.  It is now cold water, even though it's in the hot-water pipe.  

When you turn on hot water, hot water starts flowing into the pipe from the far end.  The cold water already in the pipe must be pushed out before you feel warm water at the faucet.  How long depends on faucet flow rate, length of pipe, and pipe diameter squared.   

That "square" rule is a real problem.  Go from 3/8" to 1/2" pipe, your delay doubles.  Go from 1/2 to 3/4, it doubles again.  And some dummies think 3/4" pipe is deluxe and will give them better showers.  Nope, it just makes them wait. Downsizing pipe as much as possible will help. 

Also, you can move the hot water heater closer to (right next to) the shower or sink. That's easy with electric tankless heaters. However in practice, most tankless heaters are simply installed where the old tanked heater had been (which itself was chosen because of the ugly, awkward bulk of the unit) -- in which case obviously there's no speed improvement, and speed may be worse since flow rate is limited on on-demand units.  The solution is to install the tankless unit much closer to the point of use.