I notice from sermonindex's response, that he is thinking of Adam (and Eve - God brought Eve to Adam Gen 2) and perhaps, Isaac (Gen 24).
But there are other accounts in the Bible of things happening differently. For instance, when Jacob ran away to his uncle's home, he met Rachel. And from Leah's point of view, God brought her husband to her, too. (Gen 29)
Then, there is Judges 19 - 21. This is a chilling story (which has a great deal in it to consider, to understand the culture in which it happened), but nevertheless, you'll see where 'finding a mate' comes in, if you persevere.
You should also give some consideration to the instructions God gave Levi (the priests), because we are priests.
13 And he shall take a wife in her virginity.
14 A widow, or a divorced woman, or profane, [or] an harlot, these shall he not take: but he shall take a virgin of his own people to wife.
I believe that under the New Covenant, all these conditions (states of a woman or man) become a matter of spiritual rather than physical importance, since Jesus died for our sin(s), to those who receive Him. The washing of regeneration rectifies people who receive it. (Titus 3:5)
If you do a word search of 'to wife' in the KJV, you will find references which should make you see how un-lovey-dovey matchmaking was, at times.
In contrast to this, read one of the constraints under the Old Covenant, of those who took it upon themselves to choose their own sexual partner without having married her first.
Then the man that lay with her shall give unto the damsel's father fifty [shekels] of silver, and she shall be his wife; because he hath humbled her, he may not put her away all his days.