The protocol of 1 hour before procedure is not arbitrary assuming the intent is have peak concentration during the procedure to avoid blood borne bacteria from gaining a foothold. Amoxicillin has a relatively short half-life at around 1 hour.
See NIH article...
https://www.ncbi.nlm.nih.gov/books/NBK482250/
Pharmacokinetics
Absorption: Amoxicillin exhibits stability in the presence of gastric acid and is rapidly absorbed after oral administration, with average peak blood levels typically reached within 1 to 2 hours.
Elimination: Amoxicillin has an approximate half-life of 61.3 minutes, and about 60% of the administered dose is excreted in the urine within 6 to 8 hours. Co-administration of probenecid can delay amoxicillin excretion, as the majority of the drug is eliminated unchanged in the urine.