So, you've found out there's another class. At least, officially. Though Dungeons & Dragons offer many classes to explore, one more never hurts, and not many newcomers are aware of it, despite not being a new class or anything. The expansion book Tasha's Cauldron of Everything has the Artificer, who mixes magic with science, capable of unique inventions that benefit them and their allies.
However, mechanical prowess is not the only thing you need for your character. A fun backstory is also essential, and a technology-based class opens up exciting opportunities for your character's origin.
10 Scientist
Let's get the most obvious choice out of the way. A character who does not believe in the mysticism of magic and believes it can be understood, explained, and controlled, but not in the vague way Wizards try to channel.
No, they wish to quantify it and know, with precision, what can and can not be done through magic. A simple way to justify your character's ways and to have funny interactions that annoy the other spellcasters in the group.
9 Non-Believer
Similar to the previous idea, but instead clashing with your Clerics and Paladins. A character who believes they need science to achieve actual progress and better humanity rather than look up to the Gods and try to improve the world in their own way.
It's hard to use the term Atheist in D&D since Gods appear throughout campaigns, but it would be a character that doesn't believe them in the sense of not believing they are helpful to mortals. But adding the Religion vs. Science dilemma in your story can cause exciting consequences in the campaign.
8 Inventor
You can use this idea to try convincing your DM if they say there are no guns in the scenario. You can be the first to create a new type of technology, such as the aforementioned firearms, potions, or constructs, and try your best to make them known, thus adventuring worldwide.
Then, your goal can be money, so you can fund yourself or find someone willing to sponsor you and your inventions. Can you imagine having your guns responsible for saving the realm? Everyone will want them.
7 Exiled
Let's give the Inventor a dark twist. Something catastrophic happened during your attempts to understand magic, and it's your fault. Because of that, you had to leave your former home and now live by yourself. Or wander around, since the idea is for you to be an adventurer.
Life in isolation can even justify some of your constructs as a simple way of not being alone, and your attachment to the party can be justified for the same reason. As long as you're by your friends, the goal is not even that important.
6 Criminal
An ingenious creator who uses their magnificent inventions to commit all types of criminal activities. Perfect for infiltration, you can use them to steal, rob, or kill whoever stands in your way. Being intelligent doesn't mean being good, after all.
A backstory for evil characters or at least a more chaotic side of the spectrum, it also comes with potential criminal contacts who can help you find resources for your inventions, creating fun roleplaying scenarios.
5 Archaeologist
The ancients have been gone for eons now, with nothing but ruins of their civilization remaining across the land. Now, they stand as pieces of a complex puzzle about their lives, deaths, and the items they've left behind.
An intelligent character with an aptitude for research is quite the match for this class, and it's an easy reason for adventuring. The DM will probably like a player dedicated to discovering the world's past, too.
4 Former Experiment
Instead of testing your ideas, you are the one who was experimented upon. You are the lab rat. And after spending so much time in the hands of an evil scientist, you learned their ways, even if just a bit.
Now you can use your science against theirs, understand who you were before all this experimentation, and try to use these unforgivable experiments for good, instead of repeating the mistakes that made you what you are today.
3 Magic Item Researcher
Trying to understand and recreate items works wonderfully for Artificers. Creating unique magic items is part of their job, after all. You can specialize in it, working with multiple items for you and your friends.
Alternatively, you can have a powerful item - if your DM is okay with that - and said item works as a MacGuffin for your story, where you try to understand it while others seek to take such an item from you.
2 Military Engineer
In a world full of magic, someone is bound to weaponize it, and that someone could be you. A scientist whose job is to create the most elaborate ways to get rid of multiple people at once is a functional backstory and quite a dark one, too.
And there are a few ways you can go about it: You can be proud of your inventions and use them similar to the Inventor idea, or you can regret creating such atrocities, and you are traveling around the world to destroy your own work.
1 Unknown Power
Here's a good backstory and motivation that your DM can have fun with. You've managed to find and tap into an unknown power source. An item, energy from another place or even dimension, but something you have no idea what it is.
Your studies involve trying to figure out what this power is, whether you're using it correctly, how to optimize said use, and what are the consequences of using such power. And your DM can create a whole background for you to uncover.