Short answer...hypothetically somewhat possible, but with a few gates that would probably make it difficult if not impossible to pull off.
I took a few quick looks at the financial regulations and the first issue is that if you show up in 2025 looking for an entry in 2026, even if you sign agreement in late 2025, you still have to report your 2025 financial activities just like you had already signed up. So you don't get 2025 for free. So hypothetically you get remainder of 2023 and all of 2024 without oversight.
But I see other practical problems. Working backwards, you need approval to join to series. You are at the mercy of others to agree and let you in. As we have seen (Andretti) that is not an easy tasks. Being told "no" is a real possibility. So what might you do that might cause enough drama that you are told "no"?
That leads to the next issue. You would need to fund, staff and have physical resources in place. Short of having this already done, under a dormant volcano in a secret lair in the Pacific somewhere, all of this would be very public activities. So F1 (teams, FIA, etc.) are not dumb and would know what is going on. So why would the F1 as a whole just say "yes" to someone who tries to game the situation like this? That would never fly. Lastly, take this story to your board of directors for funding and say you plan to game the system, spend a huge amount of money up front, but you have no guarantee that you will be able to secure an entry? Who in their right mind would approve that spend?
You didn't ask, but there is a similar question on the power unit side. Those are governed by a different set of financial regulations and this scenario is actually maybe planned for. In my quick reading of the regulations, there is not just a one year look back, but a look back that I think extends to effectively now. So you can join late, but the financial constraints (reporting, etc.) is just as if you had joined with the initial group who signed up for 2026 power units. The only adjustment is that you get to turn in your yearly financial reports late (others have yearly deadlines)
Richard