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That sure looks like a hydrangea macrophylla. Pulling won't work; you need to dig it out. As a shrub, it has a well-developed root system. Either a long-handled shovel or a spading fork would be my tool of choice. If you dislike it because it doesn't bloom, know that it is easy to make the mistake of cutting down next year's flower canes. They look like dead leaf stems so it is an understandable mistake. (check images online of hydrangea in winter) Hydrangea have unique pruning rules and those dead-looking stems are leaves and flowers for the coming year.

We have put our heads together here at Gardening Know How and have not been able to make an id.
This does appear to be a tree, shrub or plant that is reseeding into your yard.
Check the neighborhood and see if you can identify the culprit. Wind or birds could be moving these seeds to your yard.
Also you can take a sample or these images to your County Extension Office.
They may have an answer of what is reseeding in your exact area. They may also be interested in a plant or tree that could become invasive.

https://www.gardeningknowhow.com/extension-search

These leaves are not correct for Mile a Minute vine.

https://www.gardeningknowhow.com/plant-problems/weeds/controlling-mile-a-minute-weeds.htm

I'm sorry but we are not able to id this vine that you have.
I would take a sample to your County Extension Office.
https://www.gardeningknowhow.com/extension-search

Yes, it looks like you have some Lambsquarters in there. This weed is easy to remove by pulling it out.

https://www.gardeningknowhow.com/plant-problems/weeds/lambsquarter-control.htm

We have put our heads together here at Gardening Know How and think we are seeing your plant as Ligustrum ovalifolium or Green Privet.

https://www.gardeningknowhow.com/ornamental/shrubs/ligustrum/growing-ligustrum-shrubs.htm

This link will help you research all your weeds.

http://ipm.ucanr.edu/PMG/weeds_intro.html