I’ve been given a case to generate leads with a budget but I’ve never done this before. Any advice?

I'm currently in an interview process to move from an email marketer to a more general growth / CRM marketer. The job responsibilities are basically the same when it comes to email and customer retention so I know how to do most functions. What I'm a little stumped with is lead generation (with a budget). I don't have any experience with this so I'm not sure where to start. The company makes one product and the case they've given me is essentially as follows:

– Generate 100K email leads in 1 month with a budget of $10K (taking into account lead quality, channels, lead magnets, impact on other acquisition efforts)

I know how to convert and retain email contacts but I've never had to generate leads let alone given a budget to do so. Any advice on how I could go about making a plan for this or where I should even start? Thanks!

Edit: 100K leads as in email newsletter sign ups. Hypothetical answers, or even "you should start by thinking of X, Y, Z" is helpful!