SQL Server 2019

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create table t (name varchar(10), token int, date date);
insert into t (name, token, date) values
  ('John', 7, '2010-04-30'),
  ('John', 7, '2011-04-30'),
  ('John', 9, '2011-05-30'),
  ('John', 9, '2012-07-30'),
  ('John', 9, '2015-01-30'),
  ('John', 7, '2016-10-01'),
  ('John', 9, '2016-11-03'),
  ('John', 9, '2018-01-01'),
  ('John', 7, '2021-09-09'),
  ('Alice', 9, '2019-03-01');
10 rows affected

select * from t;


name
token
date


John
7
2010-04-30

John
7
2011-04-30

John
9
2011-05-30

John
9
2012-07-30

John
9
2015-01-30

John
7
2016-10-01

John
9
2016-11-03

John
9
2018-01-01

John
7
2021-09-09

Alice
9
2019-03-01


with
g as (
  select *,
    sum(inc) over(partition by name order by date) as grp
  from (
    select *,
      case when token <> lag(token) over(partition by name order by date) 
      then 1 else 0 end as inc
    from t
  ) x
)
select g.name, min(g.date) as min_date
from g
join (
  select name, max(grp) as max_grp from g where token = 9 group by name
) m on m.name = g.name and m.max_grp = g.grp
group by g.name



name
min_date


Alice
2019-03-01

John
2016-11-03

name	token	date
John	7	2010-04-30
John	7	2011-04-30
John	9	2011-05-30
John	9	2012-07-30
John	9	2015-01-30
John	7	2016-10-01
John	9	2016-11-03
John	9	2018-01-01
John	7	2021-09-09
Alice	9	2019-03-01