Ryder here, from the Social Care Team at Shopify. Welcome to the Community and thanks for posting! Since your shop hasn't been officially closed, we're unable to provide temporary access to obtain your invoices.
The only way this can be achieved is by switching from the paused plan to another plan. However, you'd still be able to revert back to pausing your shop afterward - and the paid subscription amount should then be credited to your account for future months when your shop is out of pause status. If you'd like to confirm that the paid subscription was credited to your account appropriately, please contact our Support Team by logging in and selecting your shop. A Support Advisor would be happy to review your account with you.
Please let me know if there's anything I can clarify.
If you decide to close your store, you'll want to go into your Admin > Settings > Billing first to download any invoices you're requiring before shutting down your store.
If you've already closed your shop, you can contact our Support Team through the Help Center by logging in and selecting your shop. One of our Support Advisors can provide you with temporary access to the account to download your invoices.
Hope this helps!