It's not "one thing" option, you can do most of those, even all of them.

So what should I do with this extra kid?

Kind of like saying the best birth control is abstinence. Technically true, but most people are going to have kids anyway. As long as we stay around replacement rate, which most western countries are at or below, having kids is a good thing so that society can keep going as people (ideally) retire. So while we're all still here, how can humans lessen our emissions. That's the question.

I know a vegan with like 6 kids who tries to lecture me for eating meat.

"Overpopulation" is simply one perspective on the problem of overconsumption. It's the lazy option, because esp. childfree people can pretend they tOTallY would've had 5 children, but they valiantly put the planet before their personal wishes. Incidentally, those same people then do nothing else and smugly point at other people. The truth is you didn't want to have children anyway, so you saved 0 CO2. I say this as a childfree person myself.

We can either reduce consumption or reduce population. I find only one of these has a chance to happen ethically, without, you know, genocide.

The graphics 58,6 tonnes of CO2 equivalent per Year and Child are 266,25% higher than the average americans 16 tonnes and 1365% higher than the global average of 4 tonnes.
~~What are the assumptions on that hypothetical child's lifestyle? Will it roll coal and eat beef jerky 24/7?~~
The Guardian article says that

figure was calculated by totting up the emissions of the child and all their descendants, then dividing this total by the parent’s lifespan. Each parent was ascribed 50% of the child’s emissions, 25% of their grandchildren’s emissions and so on.

Considering the global total fertility rate dropping from now 2.42 childs per woman to 1.66 in 2100, a global sex ratio of 101:100, average age at first child of 28 and a global life expectancy of currently 74.3 years (82.1 in 2100) my crude calculation would look like this:

  0.5    * 4t * (74.3 +  28 * ((82.1 - 74.3) / (2100 - 2023))) / 74.3
+ 0.25   * 4t * (74.3 +  56 * (     7.8      /      77      )) / 74.3 * (2.42 -  28 * ((2.42 - 1.66) / (2100 - 2023))) / (201 / 100)
+ 0.125  * 4t * (74.3 +  84 * (     7.8      /      77      )) / 74.3 * (2.42 -  56 * (    0.76      /      77      )) /   2.01
+ 0.0625 * 4t * (74.3 + 112 *           0.1012               ) / 74.3 * (2.42 -  84 *            0.0098              ) /   2.01
+ 0.0313 * 4t * (74.3 + 140 *           0.1012               ) / 74.3 * (2.42 - 112 *            0.0098              ) /   2.01
+ 0.0156 * 4t * (74.3 + 168 * 0.1012 ) / 74.3                         * (2.42 - 140 * 0.0098 ) / 2.01
+ 0.0078 * 4t * (74.3 + 196 * 0.1012 ) / 74.3                         * (2.42 - 168 * 0.0098 ) / 2.01
+ 0.0039 * 4t * (74.3 + 224 * 0.1012 ) / 74.3                         * (2.42 - 196 * 0.0098 ) / 2.01
====================================================================================================================================
= 2.076t + 1.148t + 0.518t + 0.228t + 0.1229t + 0.0634t + 0.0327t + 0.0168t + 0.0087t + 0.0045t = 4.2191t   @ 10 generations
                                                                                                = 4,2238t   @ 25 generations
                                                                                                = 4.2238t   @ 50 generations

Even if i quadrupled those 4.23t to match the US citizens average CO2 footprint, 16,89t doesn't even come close to the claimed 58,6.

where's my mistake?

pS: for the calculations I fixated the birth rate at 1,66 starting in generation 5 as well as the age with an estimated maximum of 123 years starting in generation 18.

Me and my childless girlfriend can ride our bikes to the Steakhouse with a clear conscious.

This graphic indicates not eating meat saves 0.82 tonnes of CO2. Going car free is 2.4. So yet again, it seems like the vegetarian option is another "fix our problems so we don't have to".

I often eat vegetarian meals, but it's not easy or cost efficient. I have gone car free and my 2012 Mustang GT has sat in the garage for a year now. I have one child, not 3. I'll stop meat entirely when I see larger polluters do their part. I can't save the world alone.

I would love to know the impact of just raising the kid to the age of 4, I did some math and the C02 needed just for the materials for 4 years of diapers is over 100 lbs of C02 alone. That doesn't even include all the C02 the factory and workers use to make them.