The best way to approach this is to find someone in your personal network who you could tap for interviews as an interview consultant, or go through a recruiting agency that can do some pre-screening for you.
Since you are small, you don't need to get too sophisticated in the screening as you likely won't attract any heavy hitters, and if you did, they might be bored.
If you go the recruiter route, be sure that they screen for basic competence (online exams, personal interviews, et cetera), then have them send you a pool of candidates that you can screen to see if they are a good fit.
workplace.stackexchange.com/users/46894/Old_Lamplighter
Is there any chance to get a problem set including solutions?
No.
At least not one that would do you any good.
Anything I write here
your applicant could read and it would be meaningless that they easily answer the questions.
Also, that really isn't in scope for this forum.
If you search, you'll find sets of these questions but remember that your applicants can perform the same search you did.
Since we all don´t have an IT background it´s difficult to really check on the quality of the applicants.
Yes, but not impossible.
If you have some knowledge of your existing code you can show them some of it and ask how they would implement something new.
Another answer mentioned using recruiters, and this is a good second option if you showing them code is impractical.
workplace.stackexchange.com/users/68513/J. Chris Compton
Well, the best way to recognise a good developer (in a particular skillset), is to have an existing good developer (with that skillset) to do that for you.
But of course, this is a bootstrapping problem, you don't already have that first good developer.
Here are two kinds of approaches:
Find a good developer to give you some advice
Ok, you might not already be employing a good developer, but that's not to say you can't use one.
If you have some friends who are good developers, you can ask them to give you a hand (and offer to pay them!).
After all - who gave you the idea to use React and Node?
Ask them.
You could go to a Node/React Meetup event, network, and basically if the speakers seem competent, talk to them.
Offer them 2x the hourly rate you would be willing to pay for a developer, for them to help you find a developer - help you filter out results and interview the developer.
That's going to be easy money well spent, getting a bad developer is going to cost you far more.
You don't even need to know the person IRL, someone online should be able to conduct a review of their Github account and/or set some tests for them.
Doing it yourself Do they have a Github account?
Check that they have been writing React code on it.
Check out their Stack Overflow profile - are they actively asking/answering questions?
Are their questions sensible and not 'do my homework for me'?
Note that asking questions in itself isn't a sign of a bad developer, IMO.
I have about 200 questions on my profile -
and I think I'm a decent developer.
Do they have a portfolio of websites they have created?
Are they any good?
workplace.stackexchange.com/users/32078/dwjohnston
There are a number of assessments you could use for that, have a look at devskiller website for a sample for NodeJS tests or a free alternative .
Before progressing to interview people I would ask them to do an online assessment on a testing website.
If you are afraid that they may cheat ask people to sit test in house and accommodate extra 30 mins before the interview.
workplace.stackexchange.com/users/38510/Konrad
IMHO, your first step should be an IT manager and only then a developer, or some kind of combination of two.
Be ready for lower quality or higher salary expectations than you have spent on outsource.
Spending money on consultants for task specific or time-limited contracts could be frustrating, and urge to limit expenses is always high.
But you pay for developer skill-set and experience, that rarely be available to smaller company or will be too expensive to employ including salary , employee cost and benefits.
P.S.Down-voting without comment is strange, please comment for discussion P.P.S@SambalMinion OP question
actually points out larger swarm of questions and major policy shift in the company from outsourcing to staffing development branch.
And my answer pointed out problems that can be avoided, also mentioning outsourcing cost / quality ration that need to be taken in to the account
workplace.stackexchange.com/users/78760/Strader
We are a small company and looking for a full-stack developer (NodeJS) with focus on Node and React. Since we all don´t have an IT background it´s difficult to really check on the quality of the applicants.  Is there any chance to get a problem set including solutions?
How can I identify coding skills without any IT background?
workplace.stackexchange.com
<applications><skills><code>
workplace.stackexchange.com/questions/126522
workplace.stackexchange.com/users/97961/d.meyer
You can find online assessments on testing websites. You could also find a developer outside of your company to assist with interviewing or give you advice. There are websites which offer test materials which might help you assess an applicant's skills. However, the best option is likely to be to find an expert, whether a friend or a consultant, who can help you assess an applicant's skillset.
You could find a developer, whether it be a friend or a consultant, to provide you with advice and help you assess an applicants suitability. There are sites online which provide tests that might be suitable for assessing applicants.