Yes, there is Numbers 19, much of which is devoted to the description of sprinkling with waters of cleansing in connection with sacrifice and the priest bathing after the sacrifice of the red heifer. There's a description of the Sea or Laver in 2 Chronicles 4 in which the priests were to wash, and basins for the washing of the sacrifices. And I gladly concede that these could foreshadow baptism as we read of it in the New Testament - just as Peter saw the water which floated Noah's ark as symbolic of it (1 Peter 3:20-22) and as Paul saw the parted Red Sea as its precursor (1 Corinthians 10:2).
You'll even find Naaman performing a seven-fold dipping in order to be cleansed of leprosy (2 Kings 5), but it's just not the same. Its origins are doubtless within Jewish tradition; connection with the Essene communities such as Qumran during the intertestamental period are possible.
In the New Testament, it appears first as a practice of John, Jesus' cousin - to which He accedes, though He must persuade him (Matthew 3, Mark 1:9-12, Luke 3:1-22). As Jesus and His followers adopted the practice, John quelled any rivalry by supporting it (John 3:22-36). In fact, he had earlier testified that the reason he cam to baptize was to reveal Jesus as the Son of God to Israel (John 1:29-32). And whether the relationship between belief and baptism was cause-and-effect is debatable, but there undeniably was a relationship (Luke 7:29-30).
After Jesus had been crucified, restored to life, and was about to depart again to be with the Father, He instructed His followers to go, teach and baptize (Matthew 28:19) and attached a promise to belief and baptism (Mark 16:16); and Peter was faithful to preach it come Pentecost and a powerful inSpiration (Acts 2:38). As John the Baptizer had prophesied (John 1:33) and Jesus reminded them before returning to the Father (Acts 1:5), so Peter preached that baptism and the Holy Spirit would be linked as gift with gift: the complete giving of a person's self to God; the complete giving of God's Self to that person.
Baptism into Christ is present in every story of people giving themselves to God through Christ in the book of Acts of the Apostles (2:41; 8:12-13; 8:36-40; 9:18; 10:47-48; 16:15; 16:33; 18:8). It is contrasted with John's baptism, with which the gift of the Spirit did not seem to accrue (Acts 19:1-7). In seven letters to churches in the New Testament, it is taught and preached and exemplified and enriched as the way in which God has chosen to connect us with a new life (Romans 6:4), a washed-clean life (1 Peter 3:21; Acts 22:16), a life of modeling His Son (Galatians 3:27), a life that does not end (Colossians 2:12).
None of this is commanded, exemplified, necessarily inferred, nor even directly prophesied from the text of the Old Covenant. Baptism may have been adapted from
Jesus asked His followers to observe an entirely new way for people to give glory to God in gratitude for the sacrifice of His Son, by demonstrating their faith in His death, burial and resurrection in a very tangible way, and by putting into practice a life of worship beginning with this washing of body and soul; this filling of joy and purpose and Spirit.
In short, Jesus innovated.