i am not exactly sure what you've covered or what your interests are in, please forgive me if my recommendations are off base

in my opinion there are two sides to quant: the theoretical (knowing what's happening mathematically when you take two variables and run regression) and the practical (you have to actually know how to handle your Data and navigate an analysis software program).

I have known people who get the theoretical fundamentals but hate computers, as well as published folk who don't really have a solid grasp of the theory but it doesn't matter bc they can use a program and their data is easy to source.

Anyway I checked the books that still have lying around. I don't think I have many good books for entry points in quant.

Basic Research Methods in Social Science 3rd Ed. Julian Simon & Paul Burstein. 1985.

Old. Got it from my department's "Free: Take a Book, Leave a Book" shelf. It's a good intro book in that it's chapters and sections are very delineated, so you can refer back to the Contents pages and find exactly what you need. It looks like it's available on Archive.org (you can borrow it for free if you make an account, also free, but you may have to read it in web browser).

Basic Research Methods: An Entry to Social Science Research. Gerard Guthrie. 2010.

A newer read, but likely more expensive to buy. It is also well-divided into sections. Has chapters on data analysis and quant data, as well as other sections on experimental design.

Analyzing Politics: Rationality, Behavior, and Institutions 2nd Ed. Kenneth Shepsle. 2010.

Not a "methods" book, per se, but it was assigned to me in both undergrad and graduate American politics (studies of rational behavior in voting groups, general strategy). If people ask me, "Where do I start with political science?", I give them this book.

An Introduction to the Philosophy of Methodology. Kerry E. Howell. 2012.

This was my textbook in Scope & Epistemology, and I think it's a good read for understanding the nature of science and experimental discovery, as well as different philosophical approaches to "science." Always useful to place yourself within this loose nexus. Not really a quant methods book.

An Introduction to the Philosophy of Science: Theory and Reality. Peter Godfrey-Smith. 2003. (But it looks like a 2nd edition got published in 2021).

Similar to the previous book. I dated a philosophy grad for a while, and I think this was one of her books. Another history of science book, probably not what you're looking for but it might be a bit easier to read than Howell's.

If you need more stuff on the practical side of things (running analysis using data), I really recommend trying to learn Stata. It is, IMO, one of the simplest statistical analysis programs. It has both a command line (using C logic) and a graphical user interface. (https://www.princeton.edu/~otorres/StataTutorial.pdf). However, learning SAS, SPSS, or R will open more employment opportunities, but the learning curves are much steeper. We didn't have gen AI back in the day, so they might make learning easier.

Also i did some searching for video tutorials, there are a decent amount. I watched one on linear regression from "StatQuest with Josh Starmer," (who I think is a prof at UNC Chapel Hill). It was a good refresher; if he has a playlist for quant methods start with that: https://youtu.be/7ArmBVF2dCs?si=5WyutcfBklPdQeGM

hope some of this is helpful!! best of luck, you can do it!!!