I may step on some toes, but to answer this question truthfully, I honestly think that you should introduce your child(ren) to a new partner, once the relationship has truly been defined. If you are serial dating, please do not introduce your child(ren) to multiple new partners, it's disrespectful to yourself and to your child.
If your child is two years old or twelve years old, you should consider the severity of the relationship before introducing them to your new partner. I believe I'm capable of speaking on this topic of discussion today given that I've been a single parent after conception truthfully and have fallen in and out of love, several times in my past. I've introduced my children to men before I should have probably and I've withheld my children from my partners in other instances, until it was safe to introduce them.
My point is, there is no guaranteed time to introduce your child(ren) to your partner because realistically, an organic relationship grows at it's on pace and therefore, there is no accurate timeline. I do believe that children should not be exposed to every detail of your relationship with your new partner. You can slowly introduce them to your partner and ask them age appropriate questions after they have met your new partner, to get an idea of how they actually feel about the person. Kids are like sponges and can sense negative vibes and energies so they may not be easily impressed the first time meeting your new partner, they may not care at all or they may develop a connection over a period of time, with your partner.
NFL star Russell Wilson began dating and eventually married, R&B princess Ciara, who came into the relationship with a child. The father of her child is with the rapper Future. Once her and Russell began dating seriously, the media attacked both of them: Ciara became an unfit mother and Russell was shamed for doing too much too soon in the relationship. Fast forward to today, through some custody issues settled in court eventually between Ciara and Future, Russell and Ciara have a great relationship with each other and are very present in the lives of both of their children. Russell has been a great bonus father to "baby Future" as her son is known to be called and they even have a daughter together from their marital union.
Blended families is not the easiest to do but just as with anything else in life, it requires some work and honest communication. Talk to your new partner about their expectations in your relationship. Ask them the uncomfortable questions that you need answered before introducing them to your child. Never put your partner before your child's needs. Listen to your child and address concerns if they confess anything to you after being around your new partner. I wouldn't suggest introducing your new partner to your child on the first date but possibly around the six month mark. I would also suggest that the introduction be done in a group setting to avoid your partner or the child to feel pressured to engage with one another. Again, you want this connection to happen organically.
Let your child and partner know that your partner is not replacing the absent parent they are however, a bonus to the totality of the family union. Talk to your new partner about the important concerns that comes with raising a child together: money, education, religion, discipline, etc. Never assume anything regarding your new partner. Your new partner is coming into the life of you and your child so take precautionary steps when needed and enjoy the fun times together. You can't predict a relationship's timeline or expiration date, so if you are newly divorced or separated from your soon to be ex-partner, dating can be tricky especially if you have children. Take your time getting to know your new partner first before you introduce them to your child.