Вы близки, нужно указать PublicAssistanceFundedProjectsSummaries
только ключ:
df = json_normalize(g, 'PublicAssistanceFundedProjectsSummaries')
Или:
df = json_normalize(g['PublicAssistanceFundedProjectsSummaries'])
print (df.head())
disasterNumber declarationDate incidentType state \
0 1239 1998-08-26T00:00:00.000Z Severe Storm(s) Texas
1 1240 1998-08-27T00:00:00.000Z Hurricane North Carolina
2 1240 1998-08-27T00:00:00.000Z Hurricane North Carolina
3 1240 1998-08-27T00:00:00.000Z Hurricane North Carolina
4 1240 1998-08-27T00:00:00.000Z Hurricane North Carolina
county applicantName educationApplicant \
0 Val Verde UNITED MEDICAL CENTERS False
1 NaN ATLANTIC TELEPHONE MEMBERSHIP CORP. False
2 NaN CARTERET COUNTY SCHOOLS True
3 NaN CEDAR POINT, TOWN OF False
4 NaN AURORA, TOWN OF False
numberOfProjects federalObligatedAmount hash \
0 1 12028.63 5d10528e4d343d96061da8816465e64b
1 1 30956.35 4aad896727265f6e5948a76e7977f57e
2 4 1288255.25 eb55e580a33cd4d97fa8fd1f0d71294d
3 1 4125.00 e8ed9d023142825fa658ef7b5ae4729a
4 6 22810.25 23684ce3b4d27bc7561c39b024c3a05d
lastRefresh id
0 2019-10-18T14:06:56.673Z 5da9c7005164620fcb0213ca
1 2019-10-18T14:06:56.676Z 5da9c7005164620fcb0213dd
2 2019-10-18T14:06:56.680Z 5da9c7005164620fcb0213f4
3 2019-10-18T14:06:56.680Z 5da9c7005164620fcb0213f8
4 2019-10-18T14:06:56.676Z 5da9c7005164620fcb0213da