First, you are asking, in part, a question about civil law. The position that Christians sustain to civil law, as it applies to your inquiry, pertains to Romans 13:1-7 and Acts 4:19; 5:29. In Romans 13, one learns that God authorizes the existence of government (not a specific type of politics, though), to which Christians must submit ordinarily (in all instances in which what government requires of Christians is not contrary to God's Word). In the Acts citations, specifically and only in the instances in which rulers require of Christians that they do something contrary to God's Word, can and must Christians appeal to the higher law of God. Yet, Christians who might find themselves in conflict with the government under which they live may only opt for noncompliance regarding what God through the Bible considers sinful. In all other matters, Christians must obey the government under which they live.
Second, all men now living are amenable to the New Covenant or Testament--the Gospel of Christ. The Old Testament, being fulfilled, has been replaced with the New Testament (Ephesians 2:15; Colossians 2:14; Hebrews 8:6-13; 2 Corinthians 3:6; Romans 7:6-7). Hence, our appeal in this age must be to the New Testament for authority in religion. Old Testament principles and verses that address items re-instituted in the New Testament combine with the New Testament to help us understand our role as the children of God in the Gospel Age.
Genesis 2:24 speaks to the divine institution of marriage, but does not directly speak to the scenario that you present regarding divorce and an anticipated second marriage. Deuteronomy 24:1-4 pertains to marriage and divorce under Judaism and the specific tenants therein are not re-instituted in the New Testament. Instead, Jesus Christ re-established the original institution of marriage (Matthew 5:32; 19:1-9). The apostle Paul, by divine inspiration, also addressed marriage (Ephesians 5:22-33; 1 Corinthians 7; Hebrews 13:4; Romans 7:1-3).
Regarding your questions and the summary of the biblical evidence alluded to above in the cited passages, (1) the innocent spouse (also not responsible directly or indirectly for causing one's spouse to seek sexual gratification outside marriage) of a marriage in which one's mate has committed adultery, is permitted by God to remarry an eligible candidate for marriage. (2) Christians are obligated to obey the laws of the land in which they live. (3) In the case that you propose, the law of the land does not impose a sinful requirement on the innocent spouse who may desire to remarry. (4) Therefore, though permitted by God to remarry, the innocent spouse in the narrative you presented must also obey the laws of his country.
In my country, a 12-month waiting period to finalize a divorce is not required. Actually, the laws regarding marriage and divorce vary from state to state in the USA. Still, Christians must abide by the laws that are applicable to him. Evidently, where you live, laws regarding divorce differ from similar laws in my country.
I hope this helps. Please correspond with me again if you have additional religious questions for which you desire biblical answers.