Recognise that a father’s love for his children is paramount, or should be.
Trying to compete with children for their dad’s affection is a catastrophic strategy that will end in tears – yours.
I recommend waiting at least 3 months before the introduction.
And the easiest way to ensure they stay frosty is to try bossing them around. Just because you are going out with their dad, you can’t stroll around his house like you own the joint.
Familiarity breeds contempt, and if you get too familiar in the residence the children consider their own you’ll earn their contempt.
At some point the children will become curious about who dad is dating if it looks like it is going to be an ongoing affair. Over time, if you win their respect and affection, you can offer counsel to his kids.
Sure, you have a right to be treated with respect as someone special in their father’s life, but don’t be surprised if they don’t warm to you immediately.