While the Bible does not directly answer the above question, it does give us some tantalizing clues.
Let’s start with Genesis 6:3, where God declared that man’s days shall be 120 years: “And the Lord said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.”
Now, the meaning of the “120 years” has been a point of discussion, but it is likely a statement explaining that there will be 120 years before the Flood. Some have claimed that God was setting the maximum lifespan of humans, but everyone in the line from Noah to Jacob (12 generations after Noah) lived longer than this. I guess when we finally get to heaven and can ask Jesus Himself about the proper interpretation. But the point is: this declaration was in God's mind, and the verse records that it was eventually “said” to someone–maybe Methuselah, Noah, Lamech, or Moses who recorded it.
After Genesis 6:3, the countdown was on. But this was not the same time God made a declaration to Noah to build the Ark. Let's look closer at the context.
Not until verses 13 and 14 does God speak to Noah about the Ark and coming Flood. Then in verses 17 and 18, God said, “and you shall go into the ark—you, your sons, your wife, and your sons’ wives with you” (Genesis 6:18). Notice that Noah had sons who already had wives. Noah didn’t have his first son of record until he was 500 years old, and the Flood came 100 years later (Genesis 7:6). Allowing 25–30 years for the sons to grow up and get married, we’re left with perhaps 70 years to build the Ark.
Could Noah build the Ark in 70 years? Let’s take off our mental glasses that are possibly tinted by evolutionary thinking as we make some reasonable speculations based on the Bible. Man was still a recent creation direct from the mind of God, and his intelligence not as dimmed by thousands of years of the Curse as our minds are today (and archaeology confirms that even ancient post-Flood man was capable of great feats and technological advancement). Also, people lived immense lifespans before the Flood, during which they could continually hone their talents.
Furthermore, nowhere does it say Noah built the Ark by himself. He may have hired a crew of craftsmen who used both metal and wooden tools, which the Bible records they had available (Genesis 4:22). Such tools may have been as advanced as ours today.
If it will take our team less than three years to build a full-scale wooden Noah’s Ark, it’s reasonable to think Noah could have done it in fewer than 70!