Oracle 18c

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create table it0610 (
 df_date date
);

insert into it0610 values (to_date('2022-06-03', 'yyyy-mm-dd'));
1 rows affected

insert into it0610 values (to_date('2022-06-04', 'yyyy-mm-dd'));
1 rows affected

insert into it0610 values (to_date('2022-06-05', 'yyyy-mm-dd'));
1 rows affected

insert into it0610 values (to_date('2022-06-10', 'yyyy-mm-dd'));
1 rows affected

insert into it0610 values (to_date('2022-06-11', 'yyyy-mm-dd'));
1 rows affected

ALTER SESSION  SET NLS_DATE_FORMAT = 'YYYY-MM-DD';
select *
  from it0610;

DF_DATE

2022-06-03

2022-06-04

2022-06-05

2022-06-10

2022-06-11

with dd as (
select to_date('2022-06-06', 'yyyy-mm-dd') target 
  FROM dual
) select min( d_day ) from (select dd.target -level d_day from dual, dd
connect by dd.target - level +1 in ( select df_date from it0610 
where df_date < dd.target ));
 
MIN(D_DAY)

2022-06-02

with dd as (
select to_date('2022-06-09', 'yyyy-mm-dd') target 
  FROM dual
) select min( d_day ) from (select dd.target -level d_day from dual, dd
connect by dd.target - level +1 in ( select df_date from it0610 
where df_date < dd.target ));

MIN(D_DAY)

2022-06-08