Champernowne up to me
05AB1E, 6 bytes

Code

LJ¹¡н«


Uses the 05AB1E encoding. Try it online!

Explanation

L         # Create the range [1, 2, ..., input]
 J        # Join into a single string
  ¹¡      # Split at occurences of the input
    н     # Take the first element
     «    # Append the input to the first element and implicitly output