The vertebra is the first part of the skeleton to form however it is still made of cartilage.
The first cartilage that turns into actual bone is the mandible (jaw bone). This Meckel's cartilage turns into bone 3 days before its respective muscles form:
"The sequential development of the Meckel's cartilage started as early as stage 13 (32 days) with the appearance of condensation of mesenchymal cells within the mandibular prominence. During stage 17 (41 days), the primary ossification center of the mandible appeared on the inferior margin of the Meckel's cartilage. The muscular attachments to the Meckel's cartilage in embryos were observed at stage 18 (44 days)."
Wyganowska-Świątkowska M, Przystańska A. The Meckel's cartilage in human embryonic and early fetal periods. Anat Sci Int. 2011 Jun;86(2):98-107. doi:10.1007/s12565-010-0093-3. Epub 2010 Aug 27. PubMed PMID: 20799009.
The first formation of actual bones happens at the jaw bone at day 41. Three days later the associated muscles form. This was only known recently, however this was portrayed in the Quran 1400 years before it was discovered.
Quran 23:14 "Then We developed the semen into a leech. Then We developed the leech into a lump. Then We developed the lump into bones. Then We clothed the bones with flesh. Then We produced it into another creature. Most Blessed is Allah, the Best of Creators."
Bones before muscles, this turned out to be the correct order of formation.