Logistic regression with chronologically available features
Using a predicted value would introduce bias in your models.
For me you should train 7 different models :

One with feature_day1 only
One with feature_day1 and feature_day2
One with feature_day1, feature_day2 and feature_day3
etc ...
The last one with all the feature_day1 to feature_day7

Then you have to investigate how to weight all your models to get the best predictions. I assume that your first model with only feature_day1 won't be the best, so give it low weight or don't use it at all.
You have to test different weights anyway
Normally we predict a target using static user features, here I am making serial predictions with increasing user behavior data.
I use 7 days as a period, and predict the user whether to be converted at the end of the period on a daily basis, using the feature data as of yesterday. I predict 6 times in total starting from day 2.
But this will have a problem, I'm using a logistic regression-scorecard model to train the complete historical data(of day 7s since the period's data is all available), and each feature will get a coefficient. But in production environment, feature data come day-by-day, eg. in day 2, I have feature_day1, to predict if_buy for the 1st time; in day 3, I have feature_day1 and feature_day2, to predict if_buy for the 2nd time. Technically, I can get a predicted result by setting the features of future days to null, but I doubt the correctness.  How to design this model so I can make predictions properly every day?




note
date
day_no
user_id
if_buy
feature_day1
feature_day2
feature_day3
feature_day4
feature_day5
feature_day6
feature_day7




complete_entry
20220501
7
1000
0
9
5
9
3
2
7
6


complete_entry
20220501
7
1001
1
5
4
4
9
10
10
7


complete_entry
20220508
7
1010
1
1
6
3
7
3
0
2


complete_entry
20220508
7
1011
0
9
6
3
10
7
2
2


to_predict_1
20220509
1
1200
?
6








to_predict_2
20220510
2
1200
?
6
8







to_predict_3
20220511
3
1200
?
6
8
1






to_predict_4
20220512
4
1200
?
6
8
1
5





to_predict_5
20220513
5
1200
?
6
8
1
5
9




to_predict_6
20220514
6
1200
?
6
8
1
5
9
6



complete_entry
20220515
7
1200
0
6
8
1
5
9
6
8