If the process is not so abrupt as "new life forms popping into existence", if the process is gradual, successive, subtle mutation, then we should see a fossil record that is littered with mostly "in-between" life forms. But we don't see that. We see populations distinct life forms that were here, and then they were gone.
This is actually
precisely what we see. Literally every life-form is transitional, and we have some amazing examples of change over time recorded by fossils.
You seem to believe that the fossil record is not littered with transitional fossils. This is simply not true, and if anyone told you that, they misled you.
“The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it.” - Francis Bacon"There are two novels that can change a bookish fourteen-year old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs." - John Rogers
“A world that can be explained even with bad reasons is a familiar world. But, on the other hand, in a universe suddenly divested of illusions and lights, man feels an alien, a stranger. His exile is without remedy since he is deprived of the memory of a lost home or the hope of a promised land. This divorce between man and his life, the actor and his setting, is properly the feeling of absurdity.” – Albert Camus
"...the pious hope that by combining numerous little turds of variously tainted data, one can obtain a valuable result; but in fact, the outcome is merely a larger than average pile of shit." - Barash, David 1995...
"Many that live deserve death. And some die that deserve life. Can you give it to them? Then be not too eager to deal out death in the name of justice, fearing for your own safety. Even the wise cannot see all ends." - Gandalf, J. R. R. Tolkien: The Lord Of the Rings
"The last enemy that shall be destroyed is death."
1 Corinthians 15:26King James Version (KJV)
Nihil supernum