As of 8/31/2023, some sources have Moses and Joan as parents, others have John and Joan (and some have John and Joan as grandparents), but it no actual proof and a lot of guessing.
Also, there is uploaded to Source tab Vol 6, Summer 1988 of Packard's Progress, which has a lot of English Parish records listed and on page 31 has George and Mary as parents for Samuel the immigrant's baptism.
1. This site has specific info but not actual sources posted
https://www.genealogy.com/forum/surnames/topics/packard/825/
>>George Paccard(packard) father was Moses Packard b. Abt. 1537 Earl Stonham, Suffolk, England. died in Coddenham, Suffolk, England,No death date yet, married a Joan ? 1556. Moses father was John Packard b. abt. 1492 Earl Stonham, Suffolk, England. d. Abt. October 23, 1553 in Earl Stonham, Suffolk, England. Married Joan Byrde, 1530 in Stonham, Sufflok,England.<<
2. This site is notes for a different page. If you search for 1623, you get only 9 entries, and this is about 20% down the page.
https://freepages.rootsweb.com/~gonetotexas/genealogy/Surname/notes...
>>The John Packard who may have been his father left a bequest to his son George as of 31 Jul 1557. John's widow, Joan, left a bequest to her son George as of 4 May 1591 . Marie Wyther's husband George was certainly alive in 1591 and is presumably the same George alive in 1557 when John Packard died. Therefore George would have been at least 43 years old when he married Marie in 1600 and 66 years old when he died. These ages are certainly plausible.
Stonham Aspal and Earl Stonham are adjoining towns in Suffolk Co., England. A third town which adjoins both of these is Little Stonham. It was the residence of one Aaron Packard in 1588 and 1592. The wills of both John and Joan Packard leave bequests to a son Aaron. Another town, Coddenham, is just 3 or 4 miles south of the Stonhams. It was the residence in 1585 to 1604 of one Moses Packard. The wills of both John and Joan Packard leave bequests to a son Moses.<<
3. The site George as the father of Samuel the Immigrant's father, but doesn't actually have George's parents,
https://plymouthcolony.net/families/packard1.html
4. The Packed with Packards site has specific info, but might be repeating other sources.
https://packedwithpackards.wordpress.com/2018/07/06/chapter-i-the-p...
5. FamilySearch profile has George as a Lord, son of Moses
https://ancestors.familysearch.org/en/LJ59-498/lord-george-packard%...
6. But Wikitree profile thinks that the George son of Moses don't match. (supposedly the George son of Moses from the will was a minor).
https://www.wikitree.com/wiki/Packard-18
Here is the previously linked as father Moses, who has a younger George
https://www.wikitree.com/wiki/Packard-21