There is nothing in the Scripture that says every single individual Christian must get married and have children. However, there is the creation mandate found in Genesis which is relevant and applies to Christians as a whole.
“Then God said, ‘Let Us make man in Our image, according to Our likeness; and let them rule over the fish of the sea and over the birds of the sky and over the cattle and over all the earth, and over every creeping thing that creeps on the earth.’ 27 God created man in His own image, in the image of God He created him; male and female He created them. 28 God blessed them; and God said to them, ‘Be fruitful and multiply, and fill the earth, and subdue it; and rule over the fish of the sea and over the birds of the sky and over every living thing that moves on the earth,'” (Genesis 1:26-28).
In order for people to subdue the earth, they must have children. No single individual can accomplish God’s mandate. Therefore, Christians–as a whole–are to marry, have children, and raise them to be Christian disciples who fulfill the command of God to subdue the earth although this does not require every individual be married.
Furthermore, Jesus said to make disciples of all nations.
“Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit, 20 teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age,” (Matthew 28:19-20).
This is another form of the creation mandate. As God gave the commission to Adam and Eve, the first people, so, too, Jesus gave the mandate to the first Christians.
So generally speaking, Christians are to marry and have children. Not all Christians can do this though. For example, Jesus taught that there are eunuchs for the kingdom of God.
“For there are eunuchs who were born that way from their mother’s womb; and there are eunuchs who were made eunuchs by men; and there are also eunuchs who made themselves eunuchs for the sake of the kingdom of heaven. He who is able to accept this, let him accept it,” (Matthew 19:12).
A eunuch is someone who is not involved in sexual activity, so eunuchs for the kingdom of God would not be involved in having children. Therefore, we can see that not every Christian is obligated to be married and have children.