Your post is based on a fallacious either-or premise and some other poor logic to boot. As the link from Jophiel explains, the glacial - interglacial cycles are triggered by the Milankovitch oscillations. However, these forcings just change the distribution of solar radiation both in latitude and time of year with almost no change in the global mean annual radiative forcing. Hence, the resulting changes in global climate are governed mainly by feedbacks on this. The most important feedback for the onset of glaciation is simply the growth of the ice sheets at northern latitudes (due to the fact that the summer solar radiation is no longer sufficient to prevent this) and the resulting increase in albedo. However, another important feedback is the change that is induced in greenhouse gas levels, presumably mainly through changes in the amount stored in the deep oceans. Without the warming or cooling due to these changes in greenhouse gas levels, it becomes difficult to explain the full magnitude of the warming and cooling and how the temperature change in the two hemispheres is (roughly) synchronized. From estimates of the total difference in the radiative forcings between the last glacial maximum and now and estimates of the climate response, scientists obtain an estimate of the sensitivity of the climate to a given change in radiative forcings. And, the radiative forcing due to changes in greenhouse gas levels is something that can be calculated quite accurately from basic radiative physics.
As for the sun, in the modern era we have pretty good estimates for the change in its variability and, at least over the last half century these variations are too small and don’t have the right temporal pattern to explain the warming over that time period. And, we know without a doubt that the current rise in CO2 levels is due to our burning of fossil fuels (with some smaller contribution from land use changes). There are several lines of evidence that show this: First, the ocean is not releasing CO2 in net but is in fact absorbing it and becoming more acidic. Second, the rise in atmospheric CO2 levels closely tracks the rise in our emissions and the amount of the atmospheric rise is compatible with the amount that we are releasing into the atmosphere. (In fact, if the oceans and biosphere were not able to sequester a considerable fraction of our emissions, the atmospheric rise would have been about twice as large due to our emissions.) Third, atmospheric CO2 levels are now well higher than they have been for at least 750,000 years (which covers several glacial-interglacial cycles) and likely many millions of years. Fourth, isotopic analysis of the carbon (and I believe also the oxygen) in the CO2 links it to the burning of fossil fuels.
Finally, the notion that the current rise in CO2 could be an effect rather than a cause of warming is incompatible with the ice core record, which shows a rise in CO2 levels of, at most, about 20 ppm per degree C rise in global average temperature…and even that rise seems to take several hundred years to occur (hence the observation of the “lag” of which you speak). [What that record does show us is that the current anthropogenic increase in CO2 levels and corresponding warming may lead to positive feedbacks in the carbon cycle that, over hundreds of years, may cause some addition rise in CO2 levels.