I don't think 62 will be full retirement age yet?
There are 2 different things to know about social security. People get them mixed up all the time. Social Security is saying your SS checks may be REDUCED. Not if it's taxable or not.
1. Your actual SS checks
If you are over full retirement age your actual ss checks won't be reduced. Otherwise they will actually reduce your payments if you make too much other income in the prior year. See SS FAQ for working after retirement
https://www.ssa.gov/benefits/retirement/planner/whileworking.html
First year special rule
https://faq.ssa.gov/en-US/Topic/article/KA-01927?msclkid=11bc282ccf2211ecb65078152b05ae6b
See page 5 for the special first year rule
https://www.ssa.gov/pubs/EN-05-10069.pdf
2. Income Tax (even the first year).
For any age up to 85% of Social Security becomes taxable when ALL your other income plus 1/2 your social security reaches:
Married Filing Jointly: $32,000
Single or head of household: $25,000
Married Filing Separately: 0
