There is currently petition citizen initiative underway to urge the European Commission to connect all capitals of the EU with high-speed rail.
I’ve already signed it, are you joining ?
https://europa.eu/citizens-initiative/select-language?destination=/initiatives/details/2023/000004
Edit: It’s not a petition, it’s a citizen initiative.
Maybe not high speed, but you could theoretically run a train line from Helsinki to Talinn and Stockholm. In Southern Denmark you could take the train from Rødby to Puttgarden, across the narrow stretch of water that separates Denmark and Germany. The train would just roll aboard the ferry, and then exit at the other end. As far as I know, that line has been closed down temporarily, and will run through the tunnel they’re building, when it opens up again.
More realistically, you could work to improve the train-ferry connections. The train should take you all the way down to where you board the ferry, there shouldn’t be long waits when you switch from one mode to the other and it should be seamless to purchase a ticket from Helsinki to Berlin, even if part of the trip is on a ferry.
Of course not as fast as traveling over land, but it makes more sense considering the geography, and I personally think it should count as a train connection, if the ferry is included in the train ticket.
Ireland is probably a bit more tricky.
Train ferries a bit logistical hassle through and are pretty slow and costly afaik. Another person linked a proposal for an undersea tunnel between Estonia and Finland which would solve that problem, but connecting to Sweden without a ferry is still tough, unless they decide to invest into a similar project or construct a high-speed all the way around the Baltic Sea through northern Scandinavia which is probably not really feasible.