Here I am using what is the journalistic definition of a "recession," also used in many nations although not officially in the US, where these things are determined ex post by an NBER committee. Anyway, that "journalistic" definition is that there be two consecutive quarters of negative GDP growth. Today in the Washington Post I saw a story on global carbon emissions, which are very closedly correlated with GDP, if not perfectly. Anyway, it appears that global carbon emissions hit bottom on April 7 and have been slowly rising since then (not sure about US separately, although US somewhat behind most other nations on the covid curve and so on the economic impact as well). I note that April 7 is one week into the second quarter.
This means it is very likely that at the global level we shall see positive economic growth in the second quarter, basically rising since the end of the first week of the quarter, although due to reporting lags in many countries this will not show up as positive growth in the data until later, possibly by the end of the month. This growth is slow, but it is positive, definitely not a V.
So, assuming this slow growth continues,the world will have seen a massive shock in the first quarter, with most of that in a single month, March, the largest such short term shock in recorded history by far. But it looks that it may have hit bottom quite quickly, then to turn into a slow recovery shortly after the end of the first quarter. First quarter is certainly going to be negative, but second looks very well like it might be positive, at least at the global level, hence, not technically quite a "recession" according to this journalistic definition.
The US is a murkier story. I have not seen the carbon emissions data for the US (will go check) but I am aware of one variable that may have bottomed out in mid-April, credit card orders. That is not perfectly correlated with GDP, but strongly so. The WH has made noises about it and some other less significant variables that look to have at least turned around and may be going up by now. The big one that has, and that Trump in particular focuses on, is the stock market, which certainly has come back a lot from its bottom point in late March, although still some way to go to get back to its mid-February peaks. But it is volatile and could easily go back down again, not also to forget Paul Samuelson's old wisecrack that "The stock market has predicted the last nine out of six recessions."
The Trumpists are loudly proclaiming a V shaped recovery, which really does not look in the cards, although they might get some solid growth happening by election time in November. I suspect lots of variables and also official GDP will still be negative for April, but there are two months after April in the second quarter, and while it is almost certainly doing so slowly, US GDP is almost certainly growing along with most of the rest of the world's economy now. The US might also join most of the rest of the world in having a net positive growth figure for the second quarter, if small, but no "journalistic recession": as well.