It's hard to tell without context but I don't recommend most big company jobs that are not working on things that are high risk and high reward for recent graduates normally. There's a lot of questions to be asked about what the objectives of the project are, executive backing, and (most importantly) how strong the funding is to demonstrate the worth. As an example, my customer has made huge investments in attempts to hire developers while skimping tremendously on dependent efforts that would remove barriers for those developers to the extent that most developers are doing 9-5 jobs and unable to accomplish a lot while a lot of the infrastructure teams are working 12+ hour days working on very much solved problems from decades ago that only exist due to lack of respect and understanding of basic automation principles required to scale software companies of any sort. Everyone wants to work on modern, relevant problems - make sure that people are specific about their current barriers as being technical rather than organizational as a prospective employee.

Look for a deep culture of respected and accomplished leaders in software up and down the hierarchy. If nobody in a position of authority has delivered software successfully before that you can recognize as an engineer, pass because culture and experience among executives is massively important and their priorities should focus on long term growth (Amazon was ridiculed by enterprise vendors while I screamed that they will eat their business in a decade - they don't care because they'll go somewhere else while I have to deal with the very expensive consequences of bad software). There are too many great companies around today to waste time on mediocre companies - it is better to be jobless for months or years waiting for a great company to accept you for your talents than to waste some of the best years on companies where your best efforts will result in second rate winnings. It's a huge risk to work for mediocre companies that will not put the work you will have to put in themselves.

My e-mail is djk29a on Google's e-mail service. Not sure how the first part of your e-mail works out and I'm several days late so hopefully this is relevant advice.