Hello,

The fastest way to get subscribers would be to buy the traffic. You could buy facebook ads, google ads, but if in my opinion, the fastest way would be to buy solo ads. If your squeeze page is well optimized, you could expect to get 30%-60% conversion rate, it means from 100 clicks, you would get 30-60 subscribers in one day or even faster. How well these subscribers perform on your list, its another question and I really dont know the solo ads traffic quality nowadays.

To monetize the list in short term would be also to sell solo ads, if your list is pretty big, you could generate 100 clicks per day and sell for $30. This is very easy way to make money and monetize the list, BUT in my opinion, better is to not sell solo ads and this way make big harm to your list, better try to provide value to your list and sell high quality products.(Its a long term).

Short-term, a paid product follow-up to your freebie. Long-term, more follow-up products and related affiliate products/services.

As I'm familiar with FB Ads, with the right traffic, that would be a good source of paid traffic.

You could try to post in Facebook groups and over PM send them the link, but you might get reported.

Talking about monetizing the list, the only way I see is through a series of emails & re-targeting. Also, if you're looking to sell a higher ticket product, I would recommend hosting a webinar (once your list becomes bigger).

you should promote that in a facebook groups just try it.
I had an experience with this before.

You can get more ebook subscribers with these simple ways:

1. Get Subscribers by Increasing Your Conversions: For this you need to optimize the conversation funnel. By using Email subscription call-to-action, or you can create a lead magnet by using some discount code on your ebook, or free delivery etc...

2. You can optimize your landing page with align with the referral source in design and content. for. i.e use you Facebook post which promises free demo trials or ebook subscriptions.

3. As per your ebook publication, figure out buyers persona, audience interest, age group, etc.. and navigate them on your website with various CTA. You can also use heatmap to check users click activity faster.

4. Add an Exit-Intent Popup for subscriptions.

5. You can also offer some insights of ebook with PDF options for free to convert users in to subscribers.

6. Try different CTA's on landing page with attractive colors.

7. Remove distractions & add some testimonials of your ebook on landing page.

8. Run Facebook Ads, or Google Ad Campaigns for earn subscribers.

9. List out your ebook in Inkitt, Free Discounted Books, E Reader Love, EBooks Habit, etc...

10. Do social media marketing everyday to promote your ebook & gain subscribers. Use sign up button in post or campaigns.

11. Do email marketing. Always keep your all email list clean with email verifier.

12. You can also promote your ebook with affiliate marketing.
For that you can visit the thread: How do I promote products as an affiliate

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for short term you should provide more value additonally to your free ebook and convince them for a good while to upgrade
long term you need to search for quality products in the same niche and review them in detail for your subscribers and convince them that way to get their hands on it

Beware, when you're creating free offers to build subscribers. You're attracting a lot of freebee seekers to your list.

As for your answer, paid traffic would be your best route. Whether that'd be facebook ads, PPC, or solo ads. I'm sure you'd get some subscribers fast depending on your budget.