Scientists are certain that there are no undiscovered elements missing from the periodic table from hydrogen to lawrencium. How? and why?
You are talking about the first 103 elements. An element is by definition identified with the number of protons in its nucleus, the so-called atomic number. Any atom with 6 protons is carbon, it cannot be anything else. So there cannot be any missing elements out to 103, as all of these elements have been confirm discovered by accepted scientific methods.
For example, here is a link to a CHEM Study film showing how transuranium elements (i.e. atomic number > 92 and man-made) can be separated from one another and verified as distinct.