Noah’s ark was built to save a handful of humans, so how is the ark symbolic of salvation through Jesus Christ?
Wickedness of Man
After Adam and Eve were banned from the Garden of Eden and their chance at eternal life gone, it didn’t take long before mankind spiraled into the depths of evil and wickedness. By the time Noah and his family arrived, “the LORD saw that the wickedness of man was great on the earth, and that every intent of the thoughts of his heart was only evil continually. The LORD was sorry that He had made man on the earth, and He was grieved in His heart” (Gen 6:5-6). In just over a thousand years, “the earth was corrupt in the sight of God, and the earth was filled with violence. God looked on the earth, and behold, it was corrupt; for all flesh had corrupted their way upon the earth” (Gen 6:11-12). God had to start over with Noah and his family because all humanity ever thought about was devising new ways to sin. Whatever their imagination could conceive, they would do. If God had allowed this to continue, humanity would become worse than a pack of wolves, devouring one another and only the strong would survive, so God told Noah, “The end of all flesh has come before Me; for the earth is filled with violence because of them; and behold, I am about to destroy them with the earth” (Gen 6:13),so “Make for yourself an ark of gopher wood; you shall make the ark with rooms, and shall cover it inside and out with pitch” (Gen 6:14), and “I will establish My covenant with you; and you shall enter the ark—you and your sons and your wife, and your sons’ wives with you” (Gen 6:18). The ark was their only hope of escape, so Noah and his sons began to build, and it had to be to the exact specifications that God gave him. If “every intent of the thoughts of his heart was only evil continually” (Gen 6:5-6) , then repentance would seem unlikely. The ark was the only hope for mankind. Today, Jesus is our only hope of escaping the flood of God’s coming judgment on those who reject Christ.
Man of Salvation
The Apostle Peter wrote that “God did not spare the ancient world when He brought the flood on its ungodly people, but preserved Noah, a preacher of righteousness, among the eight” (2 Pet 2:5). so apparently while Noah was building the ark he was also witnessing to the wicked world around him. The author of Hebrews wrote that it was “By faith Noah, being warned by God concerning events as yet unseen, in reverent fear constructed an ark for the saving of his household. By this he condemned the world and became an heir of the righteousness that comes by faith” (Heb 11:7). This meant that God gave mankind around 100 years (some say 120 years) to repent while Noah built the ark, and still there is no record of even one person repenting. Even so, God was patient, and today, is still patiently waiting for others to come to Christ and be saved.
The world, at least as it seems to me, is growing more and more like the days of Noah. Jesus said that one of the signs that occur prior to His second coming was just “as were the days of Noah, so will be the coming of the Son of Man. For as in those days before the flood they were eating and drinking, marrying and giving in marriage, until the day when Noah entered the ark” (Matt 24:37-38). Today is very similar to Noah’s day when “they were unaware until the flood came and swept them all away, so will be the coming of the Son of Man” (Matt 24:39). There is no shortage of scoffers today who tauntingly ask, “Where is the promise of his coming? For ever since the fathers fell asleep, all things are continuing as they were from the beginning of creation” (2 Pet 3:4). Today seems very much like the days of Noah when it seems all society ever thinks about is evil, foremost of which is the flaunting pride associated with sexual immorality.
The Ark and the Call to Christ
The Lord told Noah to put pitch on the inside and outside of the ark. Pitch is a black or dark viscous substance like tar, however the Hebrew word for pitch is “kaphar” and it’s definition is; “to cover, purge, make an atonement, make reconciliation” (Strong’s # 3722), so just as Noah was told to cover the entire inside and outside of the ark with pitch, so Jesus is our cover…our atonement, reconciling us back to God. After the ark is built, “the LORD said to Noah, “Go into the ark, you and all your household, for I have seen that you are righteous before me in this generation” (Gen 7:1). In similar fashion, those come to Christ will not be turned away (John 6:44), and those who are in Christ have no more condemnation (Rom 8:1) because they have the very righteousness of Christ (2 Cor 5:21). They are covered (kaphar) because they’ve been reconciled back to God (2 Cor 5:18). Another point is there is only one way to enter the ark and it’s through the one and only door. Jesus calls Himself the one and only way (John 14:6), which He is (Acts 4:12), and the door to His sheepfold. Jesus said, “I am the door. If anyone enters by me, he will be saved and will go in and out and find pasture” (John 10:9). If not, they have the wrath of God abiding on them (John 3:36b). Even though Noah had to choose to enter the ark, “the Lord shut him in” (Gen 7:16), showing it is God alone Who God saves us and preserves us. Any door the Lord shuts, stays shut until God opens it again, and what God shuts, no man can open. The waters represent God’s judgment, but Noah didn’t save himself…it was God who instructed him how to do so. Today, God instructs us how to be saved and that’s by trusting in Christ. Noah trusted the ark, and we can trust in Christ. The ark was made of wood, just as the cross was. The pitch protected the people inside, making a water-tight seal, and Jesus’ blood covers our sins and protects us from the wrath of God. Lastly, God prepared a place for Noah and his family when the ark settled. Jesus said He will return for us and is preparing a place for us too (John 14:3).
I think of it less as a plan of salvation than the Man of Salvation, and of course, that’s Jesus Christ, but the ark is a type of Christ in regards to being saved. When God brings us to repentance and we place our trust in Christ, our soul is sealed by His atonement (Eph 1). Jesus’ blood makes a water-tight promise of God that no flood, no fire, or even death itself can ever separate us from God (Rom 8:38-39). The symbolism of the ark is not hard to see, and it serves as a good reminder that Jesus Himself became our covering; just as the Mercy Seat covered the Ark of the Covenant.
Here is some related reading for you: How Did Noah Fit All The Animals In The Ark? A Bible Study 
Resource – Scripture quotations are from The Holy Bible, English Standard Version® (ESV®), Crossway Bibles. (2007). ESV: Study Bible : English standard version. Wheaton, Ill: Crossway Bibles. Used by permission. All rights reserved.