No
Manifest Echo, second bullet point (emphasis mine)::
When you take the Attack action on your turn, any attack you make with that action can originate from your space or the echo's space. You make this choice for each attack.
There is nothing in Manifest Echo that changes who makes the attack. The echo is not making an attack, but your attack originates from the echo's space. You are still making the attack.
Paralyzed(emphasis mine):
Any attack that hits the creature is a critical hit if the attacker is within 5 feet of the creature.
Paralyzed does not say that the attack must come from within 5 feet, but specifically that the attacker must be within 5 feet. So since it's the echo knight who makes the attack, it's the distance between the target and the echo knight, the attacker, that matters.
We can compare this to the third bullet point in Manifest Echo(emphasis mine):
When a creature that you can see within 5 feet of your echo moves at least 5 feet away from it, you can use your reaction to make an opportunity attack against that creature as if you were in the echo’s space.
This opportunity attack is made as if you were in the echo's space. This wording is not present in the second bullet point. Since they use this wording here, it's reasonable to assume that they would have used the same wording in the second bullet point if the attack was meant to be treated as if the echo knight was in the echo's space.