To find the smallest number we first arrange the given digits in ascending order.

0 < 1 < 4 < 6 < 7

Since we cannot write a number starting with '0' we have to write it in 2nd position.

So our required order will be 1, 0, 4, 6, 7.

We have to make the smallest 7 digit number using the given digits, so we need 2 more digits.

To make the smallest 7 digit number we will use 1, which is the 2nd smallest digit ($\because$ we have to make the number without repeating 0).

So the smallest 7 digit number using the digits 4, 0, 1, 7, 6 without repeating 0 is 1011467.