Your best bet is to try these discords. If you're planning to take raiding seriously in FFXIV I'd strongly advise getting familiar with both of these discord servers. While other servers do exist, these are universally considered to be the main raid discords:
FFXIV Recruiter: https://discord.gg/ffxivrecruiter
FFXIV The Balance: https://discord.gg/thebalanceffxiv
If you're uncomfortable with links, just google FFXIV Recruiter or FFXIV The Balance Discords. Fill out whatever random information they ask you upon joining and select your server roles. I think Recruiter actively kicks people out who remain role-less or something. They change their policies a lot.
Once You're set up:
FFXIV Recruiter: Scroll down in the channels section and look for "Static-lfg" and "Static-lfm". lfg means 'Looking for group' and lfm stands for 'looking for more'. Under "static-lfg" you'll write out and post a self-advertisement of yourself looking for a static. In this channel, you write out a resume of yourself, and static leaders if interested in you, will send you a DM over Discord. If you're unsure of what to write, you can never go wrong with mirroring what others write. Just try not to copy exact texts but it's perfectly okay to recycle what others say as a base. "Static-lfm" is the opposite. The statics write out a resume of their own and you browse/window shop through ads until you find one that interests you and you send them a DM. Something along the lines of, "Hey, I saw your recruitment post on FFXIV Recruiter, are you still seeking members for the role you're looking for? I am interested." is good enough. You could add more information but usually checking to see if they are still recruiting first is okay. You will be expected to follow up with some information such as your FFlogs. If you don't have any FFlogs then be honest that it's your first time doing Savage at all. My recommendation is to start with a casual static because most midcore-hardcore groups are going to be stingy about having a paper trail of logs. It is considered server etiquette to use the server emojis for your job icon instead of writing your job name out. Something like :RDM: instead of Red Mage for example.
FFXIV The Balance: Is more or less the same as above but instead of looking for "Static-lfg" and "Static-lfm" you are looking for the channels "Oce_lfm" and "Oce_lfg" or whatever other abbreviation works for your data center. You will post the same information you would for FFXIV Recruiter and you may even copy and paste the same messages into both discords.
If you don't get any hits on your ads after a day or two, I would copy to clipboard your ad, repost it, and delete your previous one. It's okay to bump yourself. Just try to do it in a reasonable timeframe so it's not spammy. It can take weeks before you find something that works for you. Worst case scenario, you can always use the same discords to make your static but I'd personally try to find one. You may have to make some sacrifices such as staying up later or raiding on days that you otherwise may not want to raid on. In the meantime, I would still try to use the party finder while you wait for a group to commit to. Look into figuring out how FFlogs work, and try to get some logs posted to make yourself look more presentatable for recruiters. Contrary to popular belief, raiding and recruitment is very akin to looking for a job so don't be surprised if it ends up feeling like one. One more piece of advice, don't be a pest. If you send someone a message and they don't reply, chances are they are intentionally ignoring you. This is quite common. While rude, many people don't like confrontation and don't want to be the bearer of bad news. Don't put all your chips into waiting for one group. Also, don't mistake having a trial as being a permanent slot. It's quite common that a lot of groups will want to try you out first to see if you are a good fit. Sometimes they may trial multiple people for the same position. It's okay for you to try multiple groups yourself, just be upfront and honest about it and once you do find a permanent slot, quit trialing for other groups. It's very frowned upon.
PS: It is expected and common courtesy for you to have Savage unlocked already before you start applying to groups. Also it may take weeks before you find a static. This is unfortunately normal. Not the best news to hear but don't let it discourage you either.
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In the meanwhile, keep trying Party Finder and if you can't find any groups, start making your own and have it accurately labeled that you are new. Check when your data center's prime time is and try to aim for your Party Finder attempts during that threshold.