Short Answer

There is no such thing as a valid assumption. Assumptions prove nothing, not even the assumptions made by a famous evolutionist. Not even if they call those assumptions, axioms. Not even if they claim that their assumptions are the correct assumptions.  Evolution isn't science.

Detailed Answer

One of the reasons that many intelligent people have trouble making good, solid decisions is that they have been educated into a mindset that believes that assumptions are some part of logic or science. Universities are teaching things like evolution and socialism that can only be supported by many assumptions and a great deal of ignoring of facts. False logic is taught in classes that claim to be teaching logic. Most of this educating into ignorance has a single focus: to try to diminish God.

Here is a conversation that illustrates this point:

Evolutionist: "The trouble with the creationists is that they make the wrong assumptions."

Student: "What makes their assumptions wrong?"

Evolutionist: "The evolutionists make valid assumptions. The creationists' assumptions are not valid."

Student: "How can an assumption be valid? I thought that an assumption was just something you make up."

Evolutionist: "Well, the evolutionists' assumptions are based on observations of science."

Student: "If it's based on observation, why would you need to make an assumption? You could just state the observation, couldn't you."

Evolutionist: "Well, we haven't been able to observe the things that we need to assume, but none of our other observations contradict the things that we have assumed."

Student: "So you are saying that you are looking for an uncheckable lie?"

Evolutionist: "No! Our assumptions are not lies! The creationists assumptions are lies! Our assumptions are, in themselves, proof of evolution."

Student: "How can an assumption prove anything?"

Evolutionist: "Stop asking me all these nasty questions! You must be some kind of religious fanatic! I can see now that you aren't intelligent enough to understand the really deep things of science and logic!"

Student: "I wish we could have a mutually respectful conversation."

(This is taken from an actual conversation)

Numbers 15:39 . . . and that ye seek not after your own heart and your own eyes, after which ye use to go a whoring:

Romans 8:7  because the carnal mind is enmity against God, for it is not subject to the Law of God, neither indeed can it be.

Psalm 53:1 The fool hath said in his heart, There is no God.

Jeremiah 17:9 The heart is deceitful above all things, and desperately wicked: who can know it?

1 Corinthians 2:14 But the natural man does not receive the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.

Proverbs 28:26 He that trusteth in his own heart is a fool: but whoso walks wisely, he shall be delivered.

Jeremiah 23:16 Thus says the LORD of hosts, Hearken not unto the words of the prophets that prophesy unto you: they make you vain: they speak a vision of their own heart, and not out of the mouth of the LORD. They say still unto them that despise me, The LORD hath said, Ye shall have peace; and they say unto every one that walks after the imagination of his own heart, No evil shall come upon you.

James 1:17 Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of turning.

Summary

There is no such thing as a valid assumption despite the efforts of so-called educators who teach many ideas that actually are simply extensions of assumptions. One example is the teaching of evolution. Evolution isn't science.