You'll be fine w/ Disco and SL's.
The main issue with Chase is picking up multiple Chase products and then stacking several approvals on top of that. Chase will be SPing your reports for the first week or so and again on a monthly basis looking for accounts. As long as you don't go overboard you'll be fine and Amex won't even report for 2 months or more.
Let’s all try to stay on topic to the op’s question.
I agree with @Obscure-Expert , you’ll be fine based on the info you provided us.
It's my favorite time of the year.... STUDENT LOANS jk kill me. Anyway my fall bill and financial aid package was released today and I want to apply for my loan before the beginning of August (my school takes 30+ days to "receive" my loans and tries to charge me a late fee). I have recently opened a Chase Sapphire Preferred and Amex platinum(soft pull) in the same day and also applied and was denied for a Citi Card so in total 2 new inquiries last month and 2 new accounts. Amex has not hit report yet but chase has. I don't want to spook chase because they approved me for a 12.5k CSP and increased my FU from 500-2000 two days after my approval. I've read horror stories about chase closing all accounts due to too many new accounts and inquires. Long story short, will I be okay to add a discover hard pull to my credit report and add a student loan. I have a checking and Freedom unlimited with chase as well. Just don't want to spook them
Lay off of the revolvers and the student loans won't hurt. Living the high life on credit while a student will. Paying for your education will not.
You added Platinum ( $550 ) and CSP ( $95 ) so AF are now significant. What is your SUB spend requirement for the next three months?
I am confused, are you applying for a Discover student loan, or a Discover card and separately a student loan?
The Discover card should wait. One of the attractions for that card is double cash back, but you will be allocating a fair amount of a relatively small spend to other cards.
As always YMMV, but I opened 5 new accounts around the same time as the CSP. 2 of them were Amex so they reported much later than the others. I never received any AA from Chase, however. Not that I would advocate poking any bears, but in your instance you should be okay.